Does appending a question mark to a declarative sentence result in a valid sentence?

Solution 1:

Appending a question mark to a declarative sentence results in a valid sentence?

Yes.

Edit

(This is just to elaborate and provide some examples. I stand by the assertion above. Here's why.)

sentence [ˈsɛntəns]
n
1. (Linguistics) a sequence of words capable of standing alone to make an assertion, ask a question, or give a command, usually consisting of a subject and a predicate containing a finite verb
[Collins English Dictionary, unabridged]

A valid sentence, then, need only fulfill one of the requirements listed above. Although we tend to think of sentences the way we were taught to in grammar school (i.e., involving at least a subject and a predicate, blah blah) a sentence doesn't have to be defined so narrowly. The following are all valid sentences:

Joe: Going to the mall?
Tom: Yes.
Joe: Really?
Tom: No, not really. Just messing with you.
Joe: Oh. You bastard.
Tom: I'm being a bastard?
Joe: Well, if the shoe fits ...
Tom: The shoe fits?
Joe: It doesn't?
Tom: Well, maybe.
Joe: Maybe?
Tom: All right.
Joe: So. The shoe fits?
Tom: Yeah.

Notice that peppered in the dialogue are declarative sentences expressed as questions. Sometimes they are used to cast doubt on the assertion, but in Joe's final line it is used as a request for affirmation.

Solution 2:

No. The sentence would not (normally) be properly constructed to be a question. You must alter the word order and typically add some sort of interrogative word like "what" or "who".

It is fairly common in English to add a question mark to a declarative statement to express doubt as to its accuracy. Like:

Bob: All Ruritanians are lazy.
Al: Really? All Ruritanians are lazy?

I'd say this is grammatically incorrect but may be rhetorically effective.