HAHAHA... yes, they often DO have to use the litterbox not long after a meal, so yup, I'd say it's a good idea to have one if you're gonna feed that cat at all!

As for particular timing... I think that's up to the individual cat. I know pretty much when to expect mine to be rummaging in the litter box... 4am is a prime time... I know from the sound AND the smells... LOL
LZ, I hope it's a mild winter too! Not sure about this one, although they say it will be.