Theoretically it's possible. Probably wouldn't even be that hard, since LAN support exists. Of course, it takes some...trickiness to get all the latency stuff. But it shouldn't be too bad at all.
However, I think headset support is probably outside the scope of RND. The implementation is pretty hard to get right, and there's already great options. (e.g. Discord, Teamspeak)
Although there will hopefully be an improved version of the already existing network multiplayer code once (which currently only really works from the command line on Unix systems), chat support via head set is indeed out of the scope of R'n'D (and should then just be established with already working solutions, like Skype).