Not according to my experience. Give it a try yourself and let us know what you found---you can use one of the tubes to experiment.
I'd really like to understand your experience because I can't even imagine the problem relating to IPD. My face is not symmetrical so my lens centers for eyeglasses are adjusted accordingly. But the distance between my pupils is a straight line with a certain distance, so I have no trouble aligning each exit pupil and eye pupil when using binoculars.
I don't know what you mean by using one of the tubes to experiment. For example, with a bin with a single hinge, if you move one side it is equivalent to moving the other side. All you do is change the IPD. It can be correct, too wide, or too narrow. For a bin with two hinges, you can adjust the barrels individually relative to the focus knob, but again, it makes no difference except ergonomically. With the Leica 8x20 Ultravid, to quickly position the focus knob under my finger, I unfold one side all the way and the other side only enough to get proper IPD (see attached images). It has no importance for dealing with the asymmetry of my eyes, which is far less and perhaps not even in the same direction of deviation.
Perhaps the problem you have is with one or both eyes individually, fitting the eyecup to your face. For example, for someone with a large high nose and deep-set eyes that are very close set, a large diameter eyecup may bonk against the nose, preventing proper alignment of the exit pupil with eye. I wear glasses, so don't use the eyecups, so looking through two exit pupils that are my IPD apart is no different than looking through two holes punched in a piece of paper that are my IPD apart. As long as the holes are my IPD apart, it doesn't matter where you punch them in the sheet of paper, I can align my eyes!
--AP