If your lawn needs re-seeding this is not going to work well.

The are a few issues I see:

Grass seed requires that it be covered in some soil to germinate. This is why when trying to seed packed soil you must at least roughen the surface before scattering seed.

The other problem is that the young seedling require light to grow. If they are under a lot of grass clippings this will not be the case.

If your lawn does not require seeding then yes, some of the seeds may grow.

Grass seeds prefers sunny but cool weather. It is best seeded in the spring or fall for this reason. Not that we can't have a cool spell in June, for example, but you cannot really count it.

OK, and to bring this back to tractors, are there little reapers that would fit on a garden tractor? That would be very cool but I doubt it

I hope this helps!