Ok so I tried this several times and it always works for me:

Join MM
Tab out and bring ONLY a Media Player Classis Home Cinema window over Dota2's window

So you should have MPCHC's window and in the background Dota2

No sound is played when the MM queue is ready

We should still hear the sound

The main problem being when in fullscreen on the video, it's impossible to know when the accept window is up.