Does the engine actually not have any power when you press the accelerator at this point?

An engine idle that changes can come from various reasons. The AC coming on, a large electrical load coming on, etc. can all cause the idle to dip. Also, in OBD2 systems, the vehicle runs several monitors which can force the purge system, egr system, etc. to run a self test which also may be noticeable to the driver. These would all be normal, and may not be reproducable by a dealer. The dealer would also have no way of diagnosing this as the items I described would be normal.

Is this what is happening in this case? I don't know. I could only answer that by driving it.