Throughout the development of Ancient Greek, was σ ever pronounced as [z], perhaps when before a voiced consonant, as in ἄσβεστος?
Yes, there is evidence of this in the form of spelling confusion between Σ and Ζ before voiced consonants, which in certain contexts made its mark on Latin forms (take a look at the 98 examples of word-initial "zm" in the PHI Latin texts corpus, which appear in words taken from Greek that also have spellings with Σ, such as Zmyrna = Ζμύρνα = Σμύρνα).
Actually, confusion between these letters seems to have occurred even in other contexts, where it might not have always indicated identical pronunciation but just similarity. I can't give a great summary of this, but per Sturtevant 1920:190
Beginning with the year 340 B.C., Attic inscriptions show confusion between σ and ζ
(The pronunciation of Greek and Latin: the sounds and accents)