Sometimes yes and sometimes no.

It depends on your face and the stroke.

For example - for my cheek wtg pass I use the hand on the same side and also down the neck same side. But for up the neck it is much easier to reach and more fluid with the opposite hand.

My atg pass (ear to nose) is easier with the opposite hand but I find if I decide to go nose to ear its easier with the same side hand.

You just need to experiment to see what works best. I'm still finding new tricks to use in my pursuit of the perfect shave.