"As I am wo/man" in Twelfth Night, II, 2 (Shakespeare): a case of indefinite article omission or no?

Are "As I am man" and "As I am woman" in Shakespeare's Twelfth Night, II, 2 examples of indefinite article omission or not?

This question is (e)specially directed towards those familiar with Shakespearean English.

Voilà Viola's soliloquy in Act II Scene 2:

...How will this fadge? my master loves her dearly;
And I, poor monster, fond as much on him;
And she, mistaken, seems to dote on me.
What will become of this? As I am man,
My state is desperate for my master's love;
As I am woman,—now alas the day!—
What thriftless sighs shall poor Olivia breathe!
O time! thou must untangle this, not I;
It is too hard a knot for me to untie!

Source 1 and Source 2, which are identical.

Viola, of course, is a young woman dressed as and pretending to be a young man (called Cesario); she has fallen in love with her master (Orsino); who is already in love with Olivia, and he sends Viola (as Cesario) to court her on his behalf; naturally, Olivia falls in love with Viola (as Cesario), who describes herself as "poor monster" because she is, sort of, both (a) man and (a) woman.

It is a feature of Shakespeare's English, and one supposes that of Early Modern English, that the indefinite article is sometimes (or in some cases, usually) 'omitted' in many places where we would use it today. This includes in predicate position, when the (count) noun refers to the noun as a class, after 'ever' and 'never', and so forth. See the online Shakespearean Grammar. Other sources that indicate and exemplify this include A grammar of Shakespeare's language, A Shakespeare grammar, and, much less useful, Shakespeare's grammar. I have also consulted several annotated editions of Twelfth Night but they have been no help.

The phenomenon is said to occur in Twelfth Night in Act IV, Scene 2:

Malvolio: Sir Topas, never was ^ man thus wronged: good Sir
Topas, do not think I am mad: they have laid me
here in hideous darkness.

and

Malvolio: I say, this house is as dark as ignorance, though
ignorance were as dark as hell; and I say, there
was never ^ man thus abused. I am no more mad than you
are: make the trial of it in any constant question.

The symbol ^ indicates that the indefinite article has been omitted.

The author also happens to use the indefinite article in the same scene:

Malvolio: Fool, there was never a man so notoriously abused: I
am as well in my wits, fool, as thou art.

and also in Twelfth Night in such lines as I am ^ true knight (II, 3) and He is ^ knight (III, 4). I prefer not to include line numbers since they differ from version to version.

I think there is a clue to this just a little farther in the passage itself, where the speaker goes on to mention his "state"... and I think it is in the notion of "statehood" that these expressions (and perhaps their understanding) are to be grounded.

That is, the speaker is speaking from the state of not just being a man, but man, as in ALL men, and further, ALL (of) "man", that is, a state of mind not just identifying with all the members of that given set, but to represent them singularly, collectively, and superlatively (cf. expressions like "I am woman, hear me roar!").

Additionally, there is an allusion to "man" being used here as an abstraction, not just a concrete representative of same, or all of them, but the whole idea of being a man (or woman, later), as in expressions like "I am VENGEANCE," or similar identifications with abstractions of concrete things, or abstract concepts themselves. This identification-with-the-concept is what gives the speaker the presumed mandate to speak on that entire concept's behalf, as he indeed goes on to do throughout the quoted passage.

However, as the somewhat more modern examples above suggest, I am not sure this is so much a feature of Shakespearean English, but rather, that Shakespeare's prose simply uses more of this forceful stuff. Indeed, I would bet you a shirt frill that if H.G. Wells dumped you in ye local publick house in Merry Ole Stratford-Upon-Avon, you'd be hard pressed to hear any of the locals express such prose while quaffing their brews.

But that, of course, is pure speculation on my part. :o)