It is one of those "it depends" sorts of things. It depends on how you tolerate aspirin and it depends on what your cardiovascular risks are. I would not recommend taking it on general principal, like many in the general population do. But, you can ask your doctor if this is something that is right for you.
Obviously, if you are prone to GI bleeding or NSAID induced pouchitis flares, then the benefits of the aspirin have to outweigh those GI risks. On the flip side, not everyone who has a j-pouch has IBD and can tolerate NSAIDs fine.
Jan