I don't think it takes into account food supply, though I haven't seen peasants move into a region that was already starving.
If you see that, please report it as a bug. They're only supposed to move into areas that look like they're able to support them.
(If the region starts starving after they arrive, that's another matter; peasants aren't necessarily all that smart, and certainly have no access to the information about food storage levels—but they can tell when a place is already starving.)
