Router Placement behind TV

Anything that increases obstacles between the wireless router (or more precisely, its antenna(s)) is going to reduce its effectiveness. How much will depend on the materials, density, etc. And whether that's enough to worry about under a particular set of circumstances is hard to say.

If you want the best possible signal, avoid obstacles whenever you can. If you can’t, perhaps use an aftermarket antenna, one you can mount separately from the router itself. This is why some ppl seek out routers that specifically mention replaceable antennas; it gives them more flexibility.

My concren is would the TV generate any electric noise that would interfer with the router?

Not that I know of, but I'm not an electrical engineer either. My motto is, if it seems possible, avoid it. But considering that smart TVs often come w/ wireless built-in, and numerous other devices around the TV use wireless (blu-ray, media players, XBOX, etc.), I suspect it's not much of a concern.