That seems unlikely, I reckon it would probably decrease the total population rather than just spreading the same population over more land. In which case the decrease in land required for animal feed would probably outweigh any increase in space per animal. Note that I said 'probably' a few times, these kind of global changes can have unexpected consequences (not necessarily bad ones, mind).

Besides I'm pretty sure the US isn't currently optimizing their farming to use little land. If you were to compare the US and the Netherlands on output per square mile of arable land I reckon you'll find that there is still quite a bit of leeway in increasing production.