I suspect not. For one thing, I'm inclined to identify emotions by their phenomenal feel, so the above scenario should really be described as his feelings of anger playing the functional role of fear, etc. More importantly, though, this scenario requires that our emotions be wholly independent of the rest of our mental economy (thoughts, judgments), which is arguably incoherent. Emotions are cognitive: part of the what you experience in your anger is a judgment (e.g.) that you have been wronged.
One might respond by trying to break down these components of the emotion, the judgment and some leftover phenomenal feel. But I don't think they are so extricable (compare: what is left over in scarlet once you take away the redness?). An essential part of the overall feel comes from the judgment, so you can't subtract that without significantly altering the phenomenology.
Relatedly, I've been puzzling over a passage from Justin Oakley's Morality and the Emotions (p.19, lightly edited):
Benevolence and gratitude may both [exhaustively?] involve feelings of affection and warmth... But if one emotion can feel like another, different emotion, then the distinctions between emotions cannot be drawn in terms of feelings.
Oakley must be using 'feel' in a very narrow sense, because it seems clear to me that the different emotions have a very distinct phenomenology. But if we restrict our attention to pre-cognitive or uninterpreted phenomenal aspects, perhaps he is right. This is the sense in which duck/rabbit looks the same to you whether you see it as a duck or as a rabbit. But in a broader (and more natural) sense, they obviously look quite different, for they are readily distinguishable experiences. The lesson from duck/rabbit is that interpretation makes a difference to phenomenology (in the broadest sense). And I think the same sort of thing is going on in case of emotions and their cognitive components.