I would say accepted if edited. We need to be able to categorise it in one of the places. I would sudgest maybe making it that it from earth. Other thing, even if they are missing organs, they need to be able to feed themselves in one way or another to keep their magic flowing. So maybe basic materials of their own composure could be used and changed into their base elements for the race to feed themselves, for example a rock and fire elemental would 'ear' or 'absorb' rocks and possibly search for high heat sources to keep themselves at a acceptable energy level.
Also, for sleep, maybe placing it statist mode while doing simily sleep.
That last one is just a sudgestion. but it would be good to have them have some kind of feeding way, cause lets face it: A elemental that gets damaged will not recover unless someone gives it magic. They would need another way to recover and keep to their lives