I have had motion controls enabled the entire game. I am currently past the elite four and pretty far through all the post game content. Even so, I could not tell you a point where I have actually used motion controls.
Even doing some googling, it does appear like others are unable to figure out what the motion controls are even used for. It appears as if they are not actually used in the game. I thought they might have been usable in the contests but I have completed Master Rank on every contest and still haven't used motion controls.
In terms of vibration, no you will not miss out anything, it is just extra vibrations when things happen.