Would it work if I put a contracted sim card into a pay as you go phone?

It will, but only if the pay as you go SIM card actually works in the phone. Most phones these days tend to get locked to the network they were provided with, and sometimes even locked to the particular SIM they were provided with.

Obviously, even if it does work OK, the monthly SIM will still need to be cancelled if you don't wish to continue paying for it.