I have a Halfling Artificer (Skip N. Stone) in a homebrew campaign my wife runs and she has a human artificer in a homebrew campaign I run. So, yes. The only concern is the presence of Artificers increases the magic available to a party due to their craft reserve and Dedicated Wright (if you allow them to make one). As for races? Humans, Half-elves, Gnomes, and Dwarves would be most common artificers. The rest are traditionally tied to a form of magic (Elves) or tend to avoid magic (Half-orcs). That's not to say that they can't be an articer, merely that they would be less common.