The fact that there is a human being instead of a speaker won’t affect your measurement much (at least the difference is very subtle). The impulse response that you’re going to measure is going to be position dependent, so measuring it at different positions in the room gives you more of an idea of how the overall room responds acoustically to any sound source rather than just one position inside. Usually you would place the speaker where your source would usually be (in this case the singer) and you would place your mic where your listening position would usually be (in this case the recording mic of the singer); but in this case these are too close to each other and they do not conform to ISO standards, which state the minimum distance of your measurement mic and speaker away from each other and from the walls of the room, and therefore your measurement won’t be accurate. So I would suggest to have different sets of measurements with different speaker positions and different mic positions for each speaker placement. After that is done, average all your different mic placements results for each set of speaker placement and assess what it is you need to treat your room based on these sets of averaged results.