So THEORETICALLY, say I were to use an achievement server and get the achievement hats, items, etc., and I were to use them in crafting, could I get them back, e.g., 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.