Piezo sensors have a natural frequency and you can't push them very far off without degrading their operation.
Sound goes about 1 meter in 3 milliseconds. So if your room is 4 meters square it should take about 25ms to get a reading from a sensor (out and back). You probably have to wait for the reverb to die down, that could be another 25ms, maybe zero, maybe more. Then you can move to the next sensor. It seems reasonable that you could cycle through all four sensors 5 times a second.
A couple more issues...
- If you try to re-use a premade range finding device it might have trouble being powered up and responding right away.
- Disc type piezos can be very directional. you might go blind in the corners as people get out of the angle of view of the adjacent walls and are difficult to distinguish from the earlier and stronger opposite wall reflections. (I was assuming placement in the center of the walls, if you place in the corners this may not be true, but you might have to slow your sample rate for the longer distances.)
- I have some cylinder shaped omnidirectional (2d) piezos. They are nice for wide angle sensing, but are not very sensitive. You really have hammer them to get the signal out, and I haven't tried listening with them but I expect the are equally weak there.