"An" occurs often in Shakespeare as an alternative to "if," or sometimes in combination with it, and was apparently so used in early modern English. I don't think it has any connection to Greek ἂν, since it used is in the protasis, not the apodosis, of a conditional sentence. In Burton, it's a conscious archaism.
A few examples from All's Well That Ends Well:
Do all they deny her? An they were sons of mine,
I'd have them whipped; or I would send them to the
Turk, to make eunuchs of.
Well, thou hast a son shall take this disgrace off
me; scurvy, old, filthy, scurvy lord! Well, I must
be patient; there is no fettering of authority.
I'll beat him, by my life, if I can meet him with
any convenience, an he were double and double a
lord. I'll have no more pity of his age than I
would of—I'll beat him, an if I could but meet him again.
Good captain, will you give me a copy of the sonnet
you writ to Diana in behalf of the Count Rousillon?
an I were not a very coward, I'ld compel it of you:
but fare you well.