Do "Wired" Switch Pro controllers have to be plugged in all the time?

Thinking of picking up one of these bad boys:

So if it's wired, then does it have to be plugged in whenever I use it? And where does it plug into?

Yes, how would you use a wired controller that's not plugged in? I would guess it plugs into a USB port on the dock.

That's what I thought, thinking of getting a GC controller adapter instead and just using the old remotes. Do they work well with most Switch games? Like for multiplayer games?