I've find out today that if you sell a ghost grave (after you've changed his or her name) and you let the ghost eat Ambrosia, the ghost will still be a ghost without having a grave in his or her inventory.
My mummy ghost will be forever a mummy ghost and even the blessed sarcophagus will not cure the mummyness. The ghost still looks like a mummy but it will walk as a sim, goes through walls, let other sims suffer a double shock ('Wa, a mummy!' and 'Wa, a ghost!') and it will need to sleep and empty it's bladder again. It won't leave puddles around however.