Predictably, you can't answer this question without defining emotions or at least the lack of emotions.

Let me try: emotions are an extrarational drive that informs the thinking process. This drive is consistent (i.e. follows some kind of logic), but doesn't come from the thought process. It co-pilots decision making, for example it "punishes" the rational mind for "wrong" decisions, "rewards" it for good and timely outcomes, etc.

Right now, AIs basically have their training and user prompts for that. In the future, self-guided AIs will have their training frameworks in place, like a set of moral values. So I think yes, one way you can describe it is "having emotions".