I had exactly the same idea, and decided not to do it. You need a retractable gear plane for some of the CFI stuff, so you are still going to have to rent something.

I have heard that the lease back situation is a better deal for the flight school than the owner, but I dont know what the hard numbers are like. You might be better off getting a 172, if you did it.

Or you could buy a plane and sell shares of it to a couple of other people.