A little bit of a complicated answer. You can see the Wii games on the Wii U Pad but you still have the use the Wiimote unless you inject them with TeconMoon's Wii U VC Injector and choose to play with gamepad option, but it only works on certain Wii games that allowed gamepad support. But if you didn't make an injection like that you cannot use gamepad for Wii games at all.
So the answer is for some Wii games yes some no, and only if you create an injection and install it to your Wii U. You can't just use a Wii hard drive with Wii games and do it.
So as far as your question about running them from sd card the answer is no because you have to convert them to a Wii U VC inject and those have to be installed on Wii U internal or external hard drive. You can't play Wii U games from sd card or at least not injections.
