High power amp, does it matter at low volumes?

It’s not necessarily the power or wattage that matters, but the sustainable current into low-impedance loads—such as the 2150B amp mentioned earlier by JasonBourne. Another important factor is the rated THD+N (or SNR). For example, the Benchmark AHB2 has a THD+N rating of –118 dB (compared to –81 dB for the 2150B), resulting in a lower noise floor and less distortion at low volume. You also want to consider crosstalk. An amp with lower crosstalk typically provides better imaging at low listening levels. (–92 dB vs –60 dB: AHB2 vs 2150B)  A –60 dB rated crosstalk may noticeably smear stereo image.

A)
You have several other items to consider: 1) What is the actual volume in dba you listen too? 2) Is that volume for the whole room or just your listening position? 3) There can be considerable differences in dynamic range based upon the type of music you listen too (rock, jazz and classical). The greater the dynamic range the more power you will need.

Let’s take as an example my situation. My speakers are 89db efficient, I listen at a distance of 9 feet with a 70 dba volume never exceeding 75 dba. No one else listens so I am only concerned with the volume at my listening chair. 
One speaker produces 89 db at 3 feet, 83 db at 6 feet and 77 db at 9 feet. Two speakers produce 80 db of volume at 9 feet with 1 watt of input. You double or half the power for ever 3db change in volume. So at a 70 dba listening level I am using approximately 1/8 of a watt. 

You also must consider dynamic range. I listen to soft rock, folk and country music. So, I factor in a 20db dynamic range. Thus, for an average 70 dba listening level the amplifier should support 90 dba peaks. That means I will need 8 to 16 watts from my amplifier for the dynamic peaks.

In my case I use low powered tube amps.

B)
In my opinion with all things being equal I would choose and amplifier that doubles down into 4 and 2 ohms over one that does not.

For me, the more power you have the better the speakers will sound. No matter what volume you listen at.

In my experience, it’s very speaker specific but based upon “Welcher’s” power analysis at relatively low volumes, I would bet a Pass Labs 25 watt class A amp or a First Watt  SIT 4 or 5 would sound better than a high powered class AB amp issuing only 20 watts even on peaks. Turn the volume up loud yo even moderate levels & it becomes entirely different.

You should try it yourself & see. I think you’ll be very surprised. 

I am a low volume listener as well, but I have not experimented with low wattage amps. I was not able to find any info on your amp, so I can’t gauge how other amps might improve on it. My feeling is that you can only go so low, even if on paper you are not pushing the amp, and the lower you go the more important that doubling of wattage becomes. As others have stated, the quality of the watts matter, and it is pretty easy to best any HT integrated with decent two channel separates.