Slightly random thoughts, but I’d break this down into three answers associated with different research objectives:
(1) you are trying to model human brains and human creativity: in that case there is a lot of literature you can pin your work on in terms of how human cognition is at times general and at times domain-specific. We have many domain-specific heuristics and capabilities that may be evolutionarily innate (like social skills and maybe music capacities). Although we can turn our attention to many diverse problems some are more hidden to us than others (c.f., I recall some (tenuous?) evidence that we can better solve certain problems when presented in a social context). Even if we are applying general abilities to specific tasks, we take on much that is culturally acquired. I would also add the view that the ability to acquire domain specific knowledge through social interaction is more important to creativity (at the social level) than the classic psychology-of-creativity factors like incubation etc.
(2) you are interested in engineering creative systems for specific tasks: then it depends on the problem domain and your expectations. Do you require the system to be creative across domains? Equally, you may want to claim that the system is not just ad-hoc, in which case you have to show it. A general question here is whether general purpose creative systems are more feasible or have advantages over domain-specific ones. There is obviously the potential that by virtue of its generality such a system must have a greater creative capacity - because it is not constrained by the domain.
(3) you are interested in principle in the notion of portability between domains, in humans or in artificial systems: in that case the answer is a firm “yes”.
I think the question links to another important point and direction in CC. Systems that deal with linguistic creativity can interact with any domain. I think the work in CC in which a creative domain such as art is integrated with a language component points to a very strong direction. I’d like to see that happening in music. In recent discussions with Andrew Brown, Arne Eigenfeldt and others (in ICCC 2016 paper) we’ve been grappling with the idea that solving problems of music "sense-making” requires a linguistic level of musical though. Vague ideas, but you can look to (evolutionary) psychology thinking such as Merlin Donald for a good grounding in the relevance of this.
Ollie