There have been a number of attempts. The closest is
http://www.xrdp.org (
https://github.com/neutrinolabs/xrdp), which does basic session management against a backing Xrdp or Xvnc server, proxying either to RDP.
I haven't used it in a while (~6m), but to get the most of it you really had to compile from source and understand how to manage the various daemons (xrdp.ini is a mess, and configuring some things was rather counter-intuitive). Otherwise you wouldn't have resizable desktops (as in xrandr, not rescaling) and other niceties.
Not sure about audio, now that I think about it, but the gist of things is that so far no mainstream distribution got xrdp right or usable out of the box (unless we're talking about the niche LTSP-related stuff).