Depends on how close to max you are running.
If you are loading with max powder charges, shortest possible OAL, magnum primers, on a 100 degree day with ammo that sat in your trunk all afternoon, yes, brass can make a difference.
Thicker brass may decrease volume and thus increase pressures, but it *may* be stronger. Thinner brass may have more volume and thus lower pressures, but it *may* be weaker.
The chamber of gun can play a role too. Is it fully supported or not?