I wouldn't recommend running your wii through a capture device. There is a very noticable amount of latency involved (measured in seconds). What I would suggest, is hook your Wii up directly to another set of inputs on your tv. When added properly as a device, LMCE will create a new scenario for it, and control your TV inputs iautomatically if you select to use the wii.
Also, if you wanted to "stream" your stunning wii performance around the house for all to see, then get a splitter on the output of the wii - one side going to the new inputs on the TV, the other side going to a LMCE capture device. Then others around the house can see the game progressing, even though it will be a few seconds behind.