We have been doing this rush a lot, and I am pretty sure it doesn't lose. The only reason to not do it is because it gets boring winning every game in less than 10 mins. Both Terrans proxy reaper. I like a 7 rax reaper rush with a bunker on the mineral line, while my friend prefers the 10 rax reaper rush. Toss proxies double gate. This is incredibly strong, and will rape at least 1 person. The combo of zealots and reapers is very strong, and the pressure that it puts on all 3 opponents is often too much for them to handle.
I think good players would realize you're all behind in economy, and even if you eliminate one player they still have a shot.
1st of all, good players will scout your rush and setup at least static defense which would decimate your rush... next my rush with my friends is more effective we are ZZT or ZTT 2 6 pool rush + 1 reaper bunker rush here's the run down, our 6 pool is faster than any reaper rush, PLUS its the counter to protoss. While we are knocking down your door, reapers are in your base taking out your workers, we quickly switch players to attack. We would keep protoss for last since they are the easiest to kill in rushes.
The problem with scouting is by the time we are being scouted we are about to send units into their base. And 6 pool is not faster than proxies.