RF works by the capture effect so you will likely hear none of the transmitters and only a jumble of noise.
For those following along, it is more accurate to say that
FM receivers, not
RF in general, have a characteristic that is called their capture ratio. That is an FM receiver will
capture the strongest of two or more signals and ignore the rest.
The specification is called the capture ratio (the relative difference between the signal captured and the rest of the signals on the same frequency). This ratio is expressed in dB. Some FM receivers are much better at this than others.
In the OP's situation, the relative signal strengths of the three transmitters may to be close enough to each other to cause problems.
Now having said all of that...
It depends on the relative separation of the transmitters and FM receiver and the quality of the FM broadcast band receiver.
There are likely to be a number of variable involved. Depending on the size of room, the position of the transmitters and their relative RF outputs, reflections and so on, it
might be possible to make this work okay.
For example if the distance to the receiver for one of transmitters is 20 feet and to the other is 10 feet, the difference in signal strength would be about 6 dB. It is not uncommon for an FM broadcast band receiver to have a capture ratio in the range of 2 dB. In this case the receiver would likely lock onto the stronger signal (closer transmitter) and ignore the weaker signal.
Again there are a number of variables involved that could complicate things, but with a little thought put into the layout of the transmitters relative to the listening positions it might be possible, but there are no guarantees.
