No. It is not necessary to install OpenWRT on the 703 at all. You can switch it into " bridge" mode with the installed FirmWare. TP-Link calls this " client" mode.
You don't have to set it into bridge mode, but that's the easiest way to integrate it into an existing home network. It comes configured as an AP ( access point).
What was suggested earlier is ,that you could possibly live without the Ethnet shield and connect the 703 witho a USB cable directly to the Arduino. I have not tried this but perhaps that's another route To nvestigate.
Also, these little TP- link routers have no external antenna. Their antenna is part of the PCB. I have walked across the street and can still remotely control my project with my iphone using either of these routers from any part of my house.