I do not believe that there is any such available device at present. That does not mean that one won't be forthcoming at some point, but in order for the app to be developed also means that the TV must have the hardware to support or make provisions for the hardware from an external source for something like a microphone. Most of the apps take into account some level of the TV's video aspect as well; they deliver both an audio and video experience (camera?). To your point about being in the background, this too is a factor as if a call does come in, further logic has to be employed with regard to handling whatever the viewer was doing at the time of the call coming in. Presumably they could be watching OTA television, streaming HULU, Netflix, etc. or even on a different source for watching a DVD or using their gaming system.
There are a number of developers currently working on the issue, but none (that I know of) have reached commercial development. Do a google search for SIP client for television. I worked at a large cable television hardware manufacturer for a number of years and we actually discussed some similar scenarios, but the development costs along with the associated hardware and manufacturing costs made it somewhat of a non-starter as it would have only been a niche product in actual use.
I recall some Zenith televisions in the 70's or 80's where it accommodated a POTS line and you could answer the phone through the TV using the remote. I do not recall if you could initiate a call, but at the time it was pretty cool.
