It REDUCES the isolation at lower frequencies. So all your bass frequencies will pass through your wall BETTER than if you only have two leaves. And roughly the same as if you only had ONE leaf.Why is a 3 leave system not good (in a few words plaese)
See the graph below.
Three leaf is better for high frequencies, but high frequencies are not a problem anyway: LOW frequencies are where the problems are for us, and blocking low frequencies is ALREADY hard enough due to the laws of physics, without making it even harder by adding a third leaf.
So, if you only ever plan to play / record / mix piccolos in your room, then you'll be fine with a three lead. But if you might ever need to play / record / mix music that has things like drums, bass guitar and keyboards in it, then you have a problem. Three-leaf increases the transmission through the walls, as compared with two-leaf.
I'd suggest that you really need to figure out a way to get the inner gypsum board off that existing wall before you put up the inner wall. You might also need to beef up the outer layer of gypsum board on that outer wall, but you actually can do that from inside the wall, by adding extra gypsum board between the studs. The good news is that you can do it without ever touching the outside of that wall at all (the far left side on your drawing.)
The only other possibility is to make your inner wall extremely massive, such as several inches of reinforced concrete, or many multiple layers of gypsum board. That's the only other way to increase transmission loss: increase mass. However, you need LOTS of mass there to make up for the reduction that you are getting due to the third leaf. Don't forget that mass law says that, theoretically, you get an extra 6 dB of isolation each time you DOUBLE the mass. So going from 2 layers of gypsum board to eight layers of gypsum board will buy you an extra 12 dB of isolation. And going to sixteen layers will get you another 6 dB. And if you need yet another 6 dB of isolation, then you need thirty-two layers of gypsum board.... etc.
With a two-leaf wall, mass law does not kick in until you get down to very low frequencies, but with a three-leaf wall, it kicks in at much higher frequencies.
And that's without even considering the resonance and coincidence dip frequencies for your wall, which may or may not be big additional problems, depending on the stiffness, thickness and density of your wall.