Definitely, in fact if one theory about consciousness is correct (that it is an emergent product of "strange loops" - self-referential patterns that form in complex symbolic processing systems (whether lexical or neurological)) then the formation of such secondary minds is a simple byproduct of the creation of suitably complex mental "instances" of those minds. Effectively the pattern of symbols your mind produces to represent the character can, if it reaches a suitable level of complexity, begin to draw on the resources of your brain, sharing symbols with the rest of your mind, growing itself over time as it is used until it reaches the point where it becomes, effectively, another mind. Secondary to your own, but capable of independent thought.