Do not expect Prime, or any other dechlorinator, to remove ammonia. The statement that all of these companies use is carefully crafted. The Prime eliminates the danger of ammonia from chloramine in new water.
In essence what they are saying is that the dechlorinator will convert the ammonia temporarily to a less toxic form so that you need not worry too much about the traces that you get with your water change. The conversion is temporary since the form that ammonia takes depends more on the water's pH than anything else. Over the day or two following a water change, any remaining ammonia will assume the form dictated by the tank water pH.
For me that makes Prime a key to safe water changes because my filter will eliminate that ammonia before it has a chance to change back. For a filter that is not capable of converting the ammonia to nitrites then to nitrates, the benefit of Prime or any other dechlorinator is very short lived. Water changes are still the only way to effectively control ammonia or nitrites in a new tank, especially one going through a fish-in cycle.
I agree with this, but wouldn't using Prime be preferrable to not using a product that lessens the toxicity of the ammonia for the day or so that you are mentioning. More than likely the water change is going to need to be carried out everyday anyway, so having Prime in the water just allows the fish to suffer LESS in between water changes, and actually would enable the water change (with 0.25ppm in the tap) to actually help the fish survive the cycle. It is certainly not a miracle cure-all, but for the day or so between water changes in a fishless cycle, it would be far better than adding "fresh" water that already has toxic ammonia in it.