Tony,
Yes, they can. Here is the compatibility list for the Wii U:
Controller support:
Two Wii U GamePad controllers (newer one with a display)
Up to four Wii Remotes (includes Wii Remote Plus)
Up to four Wii U Pro Controllers
Wii accessories (Classic controller, Nunchuk, Wii Balance Board)
So, if you are now using 4 controllers (sometimes we are), they are compatible with the Wii U. One thing about Nintendo, they make most of their things backwards compatible (unlike PS and Xbox). Our son and his friends us the Wii quite a bit, but also PC based games. Some of them use the PS or Xbox, but mostly revert to the Wii due to the many games available for younger kids.
Apart from the Wii, I like to play on PC, in particular csgo and open cases on the platform
https://skin.club/community/en/articles/skins/. It's pretty fun.