Not too sure what the schools view would be.
For the CPL the A/C would need to be, as far as I am aware a complex single, i.e. retrac U/C and constant speed prop.
For the IR, although you can get a SE IR, most airlines if not all would be looking for a ME IR.
So to really utilise your own aircraft for the entire process you'd be looking at a twin, which begins to become an expensive exercise...
Some food for thought