Locked away in geologically stable layers in a time of cataclysmic climate change. Maybe there's something to that and the oceans will acidify too much for bacteria to evolve to eat the plastic, and there will forever be a "plastic layer" in the geological record to mark this era.

I was thinking more that the plastics in question are free-floating in a soluble medium and thus ripe for digestion by an opportunistic microbe.

I think you mean the "biosphere" rather than "we". Modern humans have existed anywhere from 50k-200k years. Just to put the time scales into context.

EDIT: Just to clarify: As long as disasters happen slowly enough and there are actually local maxima for the species to evolve "into", everything may be fine for "humans"... but those assumptions may be overly optimistic.