I'm not too familiar with the circumstance surrounding a permit to purchase a firearm...
If you do have a permit to purchase a firearm, is there still a check @ the time of purchase?
Hah... that's if
you get the permit to purchase a firearm.
When I lived in one town growing up my dad bought a gun every couple months because it was his hobby, and he was personal friends with the town's Chief (as much so as he knew my dad, not that they were "friends"). When we moved somewhat later, I wondered why he never bought any more, and it turns out the new town's chief was staunchly against gun ownership so while he couldn't take away my dad's guns, he knew how many my dad had, and wouldn't approve any more. (Maybe one or two in the years he's lived there since). It's not his hobby anymore obviously.
But yes, there's still a background check and waiting period after
the permit to buy (which is only good for that one gun).