Uverse wireless TV vs wired - does one slow my internet more than the other

I have 18 Mbps speed and routinely get slower than this when browsing (ie on speedtest). I also have HD TV. I have one box that is wired and two that are wireless. Both of the wireless TVs are in rooms where there is actually coax that has been run for past connections.

My question is whether or not returning to coax would save bandwidth on my wifi (ie speed up my browsing) or no benefit and just leave them as wireless.

At present it looks like the only wire entering my house from the AT&T box is an ethernet connection.