Not sure about what your definition of "feelings" are, but if you are talking about the perceptual system parrallel to thoughts and images etc ("I feel sad in this situation", or "I feel that this person is happy" while talking about another person) - then it certainly sounds like such a system would be very helpful in making strong AI.
Just from our own subjective experience we know that for certain situations, feelings are a much better match than for example visualization (even though both often go together, visuals activating feelings, feelings bringing up visual memories/scenarios) etc.
You can think of feelings as a mode-selection heuristic - most of them have direct analogues in any sufficiently adaptable system. So it's a pretty safe bet that "real AI" will have "feelings" or some reasonable analogue thereof.
