Well I'm down to 9 cats and 1 dog my all time high was 12 cats and 3 dogs. My guys were/are cat proof and my motto was simple the dogs don't chase the cats every!
Having said that, an older cat that is used to dogs would be at less risk of inadvertent injury with a puppy. A smaller kitten is going to be kind of fragile and any inter action would have to be watched for awhile.
In any case I would apply the same general rules,let the cat come to the puppy, don't let the puppy chase the cat! Small furry things running fast can kick in prey drive.
So just error on the side of caution, cat comes to the puppy, let them play but no full out ripping through the house chasing. Just do that with a kitten for a week or two and then they'll most likely be best buddies and play all the time.