If pressed for time, would this recipe work with canned pumpkin?

Yes, you could- but you would want to follow the steps in the intro for draining away any extra moisture. If you don't want to use that draining method, you could also drive off the extra liquid by cooking the puree in a non-stick saucepan until it gets really thick. It would then need to cool off completely before you finished the rest of the mix-up.