Not completely. All X10 devices on each leg will be able to talk to each other, but X10 devices on one leg won't be able to talk to X10 on the other leg. If they have a central controller, some devices will work and some won't.
Don't remove it unless they've abandoned the X10 system, or at least have abandoned centralized control.
It doesn't always have to be a central controller type system for you to have problems with X-10, many times you will have switches on one leg and the switched load on another, so the effects of removing the phase coupler can cause many switches to stop working.
A funny thing happened in one case, I had installed 4 switches to control a new flood light that was up at the peek of the gable of a 3 story house, to light up the back yard, the switches were on the main level, everything was working just fine when I left, thought to myself "cool no phase coupler needed", but what I didn't realize was the home owner was doing laundry and both her electric dryers was on when I tried the system out, after I was gone and when she was done with her laundry and the dryers were off, the system stopped working, well the electric elements in the dryers was linking the two legs together and allowing the X-10 signal to cross over, boy did I feel dumb, had to add a phase coupler and everything worked just fine.
Also just a heads up, sometimes if you are having a problem getting a signal in a room, look around for a surge suppressor strip on that circuit, if it has a RFI filter in it, it can block the X-10 signals on the whole circuit, and even the whole phase if close enough to the panel.
