Yes, but we now need to clarify "side". The experiment would be to change which side of neutral, in the electrical sense. That might or might not involve changing which side of the breaker panel, in the left-right sense.
Most breaker panels are laid out so that the electrical side, (or phase -- I have no problem referring to it as a phase) "criss-crosses" the panel, so that moving to a breaker slot higher or lower, or left or right, switches phase. Results in a checkerboard pattern.
If you think about it, it must work that way vertically, for a ganged pair of adjacent breakers to give you 220V.