Notwithstanding the issues noted above what if you pay in advance and then decide you hate flying and want whats left of your money back? Yes I am sure they will say you can get a refund less any sort of admin fee etc but how long will it take and how many frustrated phone calls will you have to make or turn up on the doorstep only to be told that so and so isn't here and to come back later.
Also what if you decide that the school doesn't suit you? Or you move house and the school isn't well located for you? Or you could have a run in with an instructor, ask for another one from the CFI and be told to go jump. Just remember that by paying in advance the school will have a hold over you and they know it.