No more than it being either directly above or directly below the TV which will most likely be putting out quite a bit of sound, and if that were a problem Nintendo probably would have noticed it by now.
Teleconferencing mics, like the ones used in Polycom conference room phones, have noise cancellation technology which cancels the sound that the device is outputting, preventing it from coming back into the mic.
People underestimate how much noise a fan can generate, especially when it's near a mic which is intended to pick up voices from 10 feet away. In the case of Polycom phones used in office conference rooms, the temperature is often regulated by a central AC unit in a maintenance room somewhere, meaning no fans or AC noise is heard.
In the case of a living room, however, it's not uncommon to have an AC unit in the window in the same room or at the very least a fan running. The WiiSpeak mic will be rendered useless by both of these. Beyond that, there's a whole plethora of background noise that a household of human beings generate which you'd be better off not broadcasting to your AC friends. It'd be confusing at best and embarrassing at worst.
The one hope I see for it is the fact that it looked to have a very long cord, meaning you could sit it next to you and possibly turn down the receive threshold.
Still, this is no substitute for a headset, as not only do you often not want an entire room full of people to be able to hear your conversations, but the closeness of the mic to the player's mouth is what allows for clear speech in an otherwise noisy room.
Unless Nintendo has licensed some new mic technology which somehow discerns unwanted background noise from regular speech, then I suspect this mic isn't the voice chat solution most of us were hoping for.
I'd love to be wrong, but I see this as a limitation of the technology which has yet to be overcome.