You should put the Wii in its stand as it has an air intake on the bottom. Putting it flat like that is not good for it.
The Wii is made to work with any setup you throw at it. Being setup standing with the stand, or without the stand, or sitting flat as well.
If you actually setup the Wii without the stand and look beneath it to see how much space there is left, and then put the stand on and check the space as well, you will notice, there is the exact same amount of space for the air to circulate from the Wii.
Plus, it just looks better without the stand in this setup.