I don't believe so. What you need is an HDMI passthrough and as far as I know only the XBox One has this. You would need 2 available HDMI ports OR some sort of HDMI splitter or hub if you don't have enough ports.
PS It is also possible the Wii could connect to the TV via another connection type such as Component or Composite BUT I'm not sure. I am trying to reach my brother who has one for his kids to find out what kind of ports and connections it has.
(He did not answer when I called)