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Yes the trigger should still work.
The MCX and MPX series of firearms are not made to Milspec tolerances. Because of this the Franklin Armory trigger may or may not function in one of these platforms. It depends entirely on your individual firearm. Lowers must be within Milspec tolerances for the trigger to operate.
I have the rattler and bfs trigger. I first installed the complete bfs and did a function check(unloaded). I found when I put it in semi and squeezed the trigger then held it in pulling the charging handle and slow releasing for the reset. The hammer struck the firing pin. Also with the hammer up I could move the selector to safety. I also held the trigger in pulling the charging handle then rotating to safety and slow released the trigger and the hammer struck the firing pin. I then installed the original sig rattler hammer back into the bfs trigger and redid the function check. It worked fine. I called franklin armory and told them the issue. They said the sig mcx lowers were not mil spec. This just my personal experience with the rattler. Install at your own risk.