The main problem I would see here is that if you run the coaxial cable over a long distance, I mean covering different RF areas, which I suspect you are trying to do.
If doing so, this is a complete mistake as broadcasting the WLAN over wide areas (and if most noticiable if these areas are separated), where devices would be connecting, and those devices don't hear other devices on different areas, you would be creating a clear case of 'hidden nodes', where multiple devices try to transmit to the same AP at the same time. As devices don't know other one is transmitting at the same time, transmission collide on the AP side and this does not respond to any of them, so devices constantly retransmitting and coliision happen.
