Based of my experience of gerbils and hamsters, there doesn't seem to be a link between feeding and playing activity, but they were always well-fed so that probably doesn't reflect anything like a state o nature.
My two cats are definitely more active when they've not recently eaten. When their food bowls are empty, they run around and play much more --- `hunger' tends to stimulate activity in them. Once they're fed, especially with something they really like and will gorge on, they tend to lie around and sleep after eating.
My understanding is that cats do this because the relatively short length of their digestive tract requires them to lie dormant for a long period to digest their food.
My two cats are definitely more active when they've not recently eaten. When their food bowls are empty, they run around and play much more --- `hunger' tends to stimulate activity in them. Once they're fed, especially with something they really like and will gorge on, they tend to lie around and sleep after eating.