The review for that device indicate that it does pass power through, however for a long run with a lot of power drawn at the other end the voltage drop over the length of the cable may become problematic. You can calculate voltage drop based on the current drawn by your Arduino and attached devices times the total resistance of the cable. (You should be able to look up the resistance per unit length of the cable you use, multiply that by the length *2 (you have to account for the cable from computer to arduino and from arduino back to computer!). )
If it looks like the voltage drop will be too great, you can always run the Arduino from an external supply. If you don't have a receptacle near the remote location you could pull a power cable alongside the cat5 (maybe 16AWG lamp cord or somesuch) from a 9V wall wart near the computer to the arduino's VIN.