Disc only, I'd say no way. PS2 is abundant, relatively cheap, and usually complete. Not to mention of 800 unique titles, maybe just maybe 250 - 300 of them would be solid but that's being generous. Lots of filler and junk on PS2. Sounds like most of them are not in good condition, either. The only really valuable PS2 games in a disc only condition would be the survival/horror titles everyone is after, but scratched up, probably only worth about half the average. Everything else is going to be pretty low.
I wouldn't do it. Not even sure that I would take them for free, because just selling that much undesirable stuff is a headache in itself.