New amps

It's possible but not for any reason than to alter the speakers reaction, tonally, to the new amp. If, for example the new amp enhances the bass too much, then you might move the speakers a bit to change the bass tone. Ditto the highs. But it seems to me unlikely. FWIW.

As a dealer who has had to swap equipment often, yes, repositioning the speakers after an amp change (or other component or cable change) may help to improve your overall system performance. This is because no item is linear. Every change shifts the tone coming out of the speakers. If you make a change and have an increase in one subset of frequencies, that affects balance and reflections in the room. Typically the placement adjustments are subtle but worthwhile to achieving the optimal experience.

For this reason also I no longer believe in swapping a component out and seeing which is better. Living with a piece and trying to design the system with it in mind helps to further uncover its strengths and weaknesses to the rest of your system.  

@whataboutbob1 

Definitely.

When I got my new amplifier, I had to move my speakers to someone else's house.

@tony1954 Best response yet!

Actually the amp has little to do with speaker setup. It is a function of the room   I believe that audio physics had information on their website for speaker setup. Not sure if it's still there