Emotions are a heuristic. Any general AI powerful enough to be useful is going to have to be full of similar heuristics if it's going to get anything done. The presence of chemicals is irrelevant.
In what way are emotions a dependency on getting anything done? The AI could be like the high-functioning sociopath who doesn't actually experience the subjective feeling of emotion but has learned all the physical cues that convey a given emotion. An AI would execute them flawlessly.