It's certainly possible. I knew a fella did his aerobatics instructor extension in his own chipmonk, just had it temporarily added to the ATO's books. Some paperwork involved, but isn't there with everything?
The main question is would you want to do the full FIC in your own aircraft? When the instructor is pretending to be "bloggs" he can throw it around a fair dose, even throw in the odd heavy landing just to prepare you for what real world instructing is like. I know I'd rather it was in the school aircraft rather than my own.