That is possible but why? You will have too much latency with this setup .

You can also add an AP connected to the switch for wireless devices like phones and also for laptops if you are moving around with it.

change out the switch to a 10/100/1000 so can get faster speeds. POE is nice if you plan on using APs or Security cameras that has POE. You are lucky that the runs are actually for networking and not for phone lines.