Unknown. If the squash you purchased were hybrid types, then they will not grow true, and you likely wouldn't want to grow them. If they were open-pollinated varieties, then they would probably grow true, but not necessarily. If the farmer grew multiple types of squashes close together, or even mixed in the same field, cross pollination can easily happen. But in a homogeneous, distance-isolated field, probably not. But then again, quite possibly. In a nutshell, forget about it.

Squash cross readily. Squash being sold by someone at a farmers' market were unlikely to have been grown at sufficient isolation distances to prevent crossing of the varieties. Like tcstoehr, I would not waste time and garden space growing those seeds.

I am an advocate of seed saving. If you wish to save squash seeds, there are ways to prevent unintended crossing.

Jim

I'll take the opposite view--save them and plant away. They may have crossed with other squash and you'll get something interesting--maybe an acorn squash the size of a hubbard or a hubbard with meat like an acorn, or something else. You also might get exactly what you expected. I am of the view that most of the seeds in a squash will have come from pollen from that same plant because the self pollen is probably closest and most common near the flower, but some pollen from other plants will also get carried in for some of the seeds.

I usually grow a couple varieties of squash and some pumpkins and save the seeds from the best specimens. My favorite squash variety was from a seed saved that turned out to be a cross between hubbard and buttercup and I have grown these seeds now for years (over 10-saving new seeds every year or two) with excellent results. On the other hand, I also like to play a little with giant pumpkins and the 2 plants I grew this year were from seed I carefully protected and crossed a couple years ago. The result was one pumpkin that is a cross between the pumpkin and a butter-hubbard, so I'm getting no size.

If you have very little space and don't want to take the chance of a cross that isn't to your liking, just plant known seed. If you like to play, plant a hill of saved seeds along with your hills of known squash and see what you get.