Does Computer science(or computationalism) has any role to play in Cognitive science or Creativity studies?
Yes. Computer science is one of central disciplines of cognitive science. In fact, the dominant, central dogma of modern (i.e., the last 50 years) cognitive science is that cognition is computation. This SEP article elaborates on this thesis:
Even if you don't think that cognition is computation, you would still likely think that computer science is relevant to cognitive science insofar as CompSci is necessary for computational modeling of any phenomena. For example, some dynamical systems theorists would use computational, dynamical models of cognitive processes, even if they aren't claiming that the mind is computing differential or difference equations. (Just like we might use differential equations to model hurricanes, even if we maybe don't think the hurricane itself is computing the equations.)
I'm less sure of what is considered "creativity studies", exactly, but I can imagine that computer science would be relevant. For example, CS -- and linguistics -- is definitely interested in questions like "How are an infinite number of expressions created from finite means?" Different kinds of grammars -- like regular grammars vs context-free grammars -- have different 'creative' powers. Creativity here is more defined in purely formal terms, as opposed to perhaps the semantic/artistic terms that you may have in mind. But, I and many others would argue, formal creativity and semantic/artistic creativity are intimately related.