To tell you my experiences, I didn't noticed any lag with the original Wii's virtual console games, when being played on a CRT. I compared them to games that I also have played on real consoles (e.g. Gradius II). It did not matter if I used wired controllers (e.g. GameCube controller) or wireless controllers (Wiimote, or Wii Classic Controller Pro attached to the Wiimote).
I have no idea if the Wii U's virtual console all of a sudden introduced input lag. So that's one thing that I'm very curious about.
One thing I know is that Wii Ware games like Castlevania Rebirth add video postprocessing when played in Wii's 16:9 mode, resulting in blurry pixels (not related to the TV's aspect ratio setting). These games are recommended to be played with the Wii set up in 4:3 mode. But there was no input lag whatsoever even in Wii 16:9.