Did a very quick and dirty test. Would not call this conclusive by any means. I pulled a couple 9v battery clips out, made a series harness from them. Then I pulled the battery cover, both batteries, and plugged the new harness into one of the two battery clips. Lil bit hokey but functional. Played a bunch of riffs from a fill-in I'm doing in a few weeks. I played through my Fractal AX8 into my wireless IEMs, into my 64Audio A6 IEMs - basically my "light portable show" rig.
Then I yanked the harness, put both batteries in as normal, and played the same thing.
Seat of the pants... I could not tell a difference. This is for songs that run the gamit from djent-y grind with pick to pretty clean finger tones, so it got a good grab bag of changes in there. Mostly used middle solo (probably 50% of the time), 3x pickups (25%), and a little bit of M+B.
I think if I wanted to really get particular about it, I'd breadboard up a switching mechanism and switch it back and forth more in real time than the way I did it. Probably would also be worth recording. But I really couldn't tell enough difference with this method to put that effort in, and time is pretty limited at the moment. If I couldn't notice a change in under an hour when running the same material and everything else being the same, that fails the "worth it" test and I don't actually personally care if I could pick out a slight difference in a graph or solo recording.
I went into this with an expectation too, so that could be playing a part.
Edit: Now that I'm thinking more about it, I have my bench DC power supply I could've just wired up and fed it everything between 9v and 18v DC just to see. Alas, I didn't have that clarity of thought beforehand.