It's not that easy. It comes down to what "the concept of infinity" means. Does Santa Claus exist because the concept of Santa Claus exists? (See my other comments in this subthread for my view of this.)
I would say he does. Santa Clause has a causal influence on the world. The image that we ascribe to 'him' (the concept) is different from the reality of it's influence but that is true for most things..
We characterize all sorts of things in all sorts of ways, trying to model the reality we perceive, but actually those models are also reality and they are not the same as the thing being modelled.
From this standpoint everything fictional exists but whether there is an 'infinite' amount of it is a super annoying question that just keeps going in circles so I don't really care so much what the answer is.
But if it's infinite then there is a god, right? :^)