Yes. The Yongnuo YN560-TX system has multiple channels and flash groups. If all of your multiple YN560-TX controllers are set to the same channel and groups as the YN560-TX compatible flashes in question, each controller will communicate with the flashes when it sends out a signal (typically at a shutter half or full press or when certain settings are changed or the "test" button is pressed).

If the flashes are set to channel 3 and flash one is set to group 1, flash two is set to group 2, and flash three is set to group 3 then setting each of the YN560-TX units to channel 3 will let you control flash one via the group 1 settings, flash two via the group 2 settings, and so on.

The nice thing is that if multiple photographers are in the same space and each is using their own copies of the same models, as long as each photographer has their controllers and flashes set to different channels they can operate totally independent of each other. This is in contrast to the optical control system used by Canon's and Nikon's traditional wireless flash system. In the optical system two photographers shooting the same brand would interfere with each others' flashes.