After unlocks & upgrades, there is no real use for gold (unless you need to purchase characters (which has been completed)).
I guess it's just stackable.
Edit: The Head Start is a useful one to purchase before each game.
I collected all 10 artifacts & after that nothing happens. The objective to collect them all is done and there's no other objectives & still at level 9. So disappointing. Just letting you know.
Here's a list of all 10 ring artifacts: Infinite Loop, Angel Wings, Twisted Root, Floating Island, Sky Clasp, Demon Claw, Ruby Shard, Caves Maw, Mystic Rocks & Idol's Curse.
In addition, here is a list of the Christmas-themed artifacts added in the December 2013 update: a candy cane, present, wreath, stocking, and a piece of holly. Once you collect all of Christmas artifacts, your character gets to wear a Christmas hat, and you can play as Santa for 60 gems.
Further addition: there are 5 Valentine's day related artifacts available in chests in a recent update as well.
Best Answer
Yes, you can. I don't think about it as "selling" the artifacts but rather having there be an additional reward for finding the artifacts. Originally, there weren't any rewards associated to artifacts but at a relatively recent update they added the additional reward (100-2500 coins, or one or two gems) to artifacts. I've collected the rewards for the ring, mask, critter, floral, relic, Christmas, Valentine, St. Patrick and Easter rewards and all of those hats are still available.
In other words: once you've earned a hat, it doesn't go away.