Can I get achievement items multiple times, or be banned for using achievement servers?

Say I were to theoretically use an achievement server and get the achievement hats, items, etc, and I were to use them in crafting, could I get them back?

Either by emailing Steam support or using achievement servers again? Also, would I get banned for using the achievement servers and asking for it back?

No once you have got the achievement item you can't get it again. Steam support aren't going to give you another one. Crafting with Achievement items makes the items untradable aswell so its a pretty bad idea to smelt the weapons down to scrap.

There have been instances of Steam Support returning gibuses to people who accidentally deleted them. But I would bet that Steam Support has seen people try to game the system this way, so you're better off not wasting your time (or losing your hats!)