Can the Wii U Pro Controller be connected to the Nintendo Switch console to use the controller in games or applications?
From the Nintendo Switch FAQ:
What controllers work with Nintendo Switch?
There are multiple controller options for the Nintendo Switch console, including Joy-Con controllers and the Nintendo Switch Pro Controller. Compatible controllers will vary per game, so be sure to check game details. You can see available accessories here.
Controllers from previous Nintendo platforms are not supported.
As noted above, the Switch has its own Pro Controller. It's more expensive than the WiiU Pro Controller, likely because it has motion controls and a Near Field Communication (NFC) reader (for Amiibo) built in.
It can work, but it'll require some money. You may need an 8bitdo adapter or something of that nature, using it, Check out My Mate VINCE for tutorials on such things - these types of adapters tend to work with Wii, Xbox & Playstation controllers as well! But i doubt it'll work with the wii u gamepad since it has it's on OS.