Yes you would just have to plug it into the appropriate starting point so that it disperses to all the jacks. (Likely where it is currently plugged in for you.)

Thanks for the reply Allan.

May I ask where you come across this  information or how you come to your conclusion?

Just from personal wiring experience!
Wall jacks throughout a house start at an initial point, are split, and then extended throughout a house. As long as you plug in your box to the starting point before it gets split and extended, then it will all work successfully.

Thank you very much for the info. It is greatly appreciated.