Will MVPs automatically switch with skins when enabled?

As the title says, if I enable randomized skins for a character but also enable the option which switches the equipped MVP when switching skins, does that make the MVP rotate with the skins or is that just for when you're equipping skins in the menu?

I would test this myself but so far I don't own more than one premium MVP per character as it'd be kinda pointless if this doesn't work. Thanks in advance!