Is it necessary to add "a" before the noun in this sentence?

Consider the sentence fragment:

...as Business Development Representative, I would...

If Business Development Representative describes a role occupied by a single person (for example, "as President" instead of "as a President" or "as CEO" instead of "as a CEO"), is an "a" required to precede the noun so it reads:

...as a Business Development Representative, I would...

There is just one Business Development Representative.

You should drop the article:

[1] ...as Business Development Representative, I would...

is exactly like

[2] ...as President/treasurer/secretary/chair/[...], I would...

Even though President (like treasurer, secretary, chair, etc.) is a count noun† in the singular, and such nouns normally require a determiner, examples like [1] and [2] are exceptional.

^{†Business Development Representative is not a single noun, but rather what CGEL calls a nominal. (In linguistics more broadly it would often be called an NP', pronounced "NP-bar"; see e.g. here.) However, the head of that nominal is a count noun in the singular, representative, so the whole nominal therefore normally requires a determiner. In general, in what follows, everything stated about President, treasurer etc. applies also to Business Development Representative.}

As far as why in examples like [1] and [2] we drop the article, there are two points—one about semantics, and one about syntax.

Semantically, President (treasurer, chair, etc.) refers to a 'unique role' held by a person in a particular situation. This means that the determiner should normally be dropped, provided the gramamtical function of President (and this is the syntactic point) is either that of a predicative complement or of a predicative oblique. In [2], President functions as a the latter, a complement of the preposition as, where the whose as phrase functions as a marked predicative complement.

In particular, a bare role NP cannot function as a subject or an object. You cannot say *Treasurer has resigned or *She questioned treasurer; you'd need some determiners, e.g. Our treasurer has resigned and She questioned the treasurer.

Discussion

Here is the relevant section from Collins COBUILD English Guides: Articles (pp. 51-52):

6.14 Special roles

Some nouns can refer to a special, unique role held by a person in a particular situation (for example, a government or business). When they are used like this, you can leave out the definite article.

...when he was President.
It was nearly 40 years before she became Queen.
...Mr John Hume, leader of the Social and Democratic Labour Party.

It would be unnatural to leave in the definite article and say 'when he was the President' or 'she became the Queen', although you can leave it in when the noun is followed by 'of'. Some words commonly used in this way are:

author                  chairman             king                          queen
best man             chairperson         leader                       secretary
boss                      director                manager                  treasurer
captain                 goalkeeper          president
centre forward    head                     prime minister

The context is very important. In a gang, one person can be 'leader'; in a football team, one person can be 'captain', 'centre forward', or 'goalkeeper'; at a wedding one person can be 'best man'; in a country one person can be 'king', 'queen', 'president', or 'prime minister'. Many other nouns can be used in this way in a particular context.

Note that when you are talking about a person rather than describing someone's role you need an article.

The President had issued a sympathetic reply.
The Queen then abandoned the project.

In

...as President I would...

we have a singular count noun, President, appearing without a determinative. This is a highly exceptional situiation, which is subject to some syntactical constraints. CGEL analzyes President in [1] as bare role NP (noun phrase). Here is a relevant passage (p. 328):

Also included in the category of NP are bare role NPs such as president, deputy leader of the party—bare in the sense that they do not contain a determiner. These qualify as NPs by virtue of occurring as the predicative complements of verbs like be, become, appoint, elect, but singular NPs of this kind are exceptional in that they cannot occur as subjects or objects, where a determiner such as the definite article the is required:

[8]   i  I'd like to be president.                                        [predicative complement]
       ii  I'd like to meet *president/the president.                                     [object]

In more detail (p. 253):

The crucial syntactic property of PC [predicative complement] is that it can have the form either of an AdjP [adjective phrase] or of a bare role NP (a count singular with no determiner, such as President of the Republic, treasurer, etc.). Usually it can have the form of an ordinary NP [noun phrase] too, but what distinguishes PC from O [object] is the admissibility of an AdjP or bare role NP.

[5]            PREDICATIVE COMPLEMENT                                   OBJECT
             i  a.  He seemed a nice guy/nice.           b.  He met a nice guy/*nice.
            ii  a.  I consider it bad advice/bad.         b.  I gave her bad advice/*bad.
          iii  a.  She remained treasurer.                   b.  *She questioned treasurer.
           iv  a.  They appointed him secretary.       b.  *They promised him secretary.

Examples [i-ii] illustrate the possibility of replacing an ordinary NP by an AdjP (adjective phrase) in the case of PC, and the impossibility of doing so with O. Examples [iii-iv] show bare role NPs functioning as PC and the ungrammaticality that results from putting them in O function: the NPs in [iiib/ivb] need determiners (e.g. She questioned the treasurer; They promised him a secretary).

The ability of AdjPs to function as PC but not O reflects the fact that a PC characteristically expresses a property, while O (like S [subject]) characteristically refers to someone or something: AdjPs denote properties but are not used referentially. Similarly, the restriction on bare role NPs reflects the fact that they too cannot be used referentially; note in this connection that they are equally excluded from subject function: *Treasurer has resigned.

On p. 255, CGEL points out that a bare role NP can function as predicative obliques, which is exactly how it functions in [1] and [2].

■ Predicative obliques

Predicative elements may occur as complement of a preposition instead of being related directly to the verb. Much the most common preposition is as:

[9]                    INTRANSITIVE                                          TRANSITIVE
          i  a.  That counts as excellent.    b.  I regard her as indispensable.                  [AdjP]
         ii  a.  She served as treasurer.    b.  They chose her as secretary.         [bare role NP]

Again the predicand is S [subject] in the intransitive, and normally O [object] in the transitive.³⁰ The complements of as we analyse as predicative obliques, and the as phrases themselves (as excellent, etc.) as marked predicative complements.

^{30The verb strike is exceptional in having S as predicand in a transitive construction: compare I regard him as a liability (normal, O as predicand) and He strikes me as a liability (exceptional, S as predicand). The behaviour of strike here correlates with its exceptional alignment of semantic roles and syntactic functions. Like regard it belongs to the field of cognition, yet it aligns experiencer and stimulus with O and S respectively, instead of the usual S and O (cf. §2.3), and this exceptional alignment in turn reflects the fact that the sense involved here is a secondary one relative to that of He struck me on the chin.}