No problem doing that. I only had a single coax input for cable. I could use it for sat by moving an internal coax jumper. Got tired of that.
I added a coax wall plate in a cabinet under the TV. I drilled a hole in the outside wall near that same wall plate and installed a weather proof outside coax connector. I connected the two with a quad shielded coax cable. Another coax cable from the wall plate to the sat receiver. And HDMI from the receiver to the TV. I have a Tailgater. It works fine with the standard RG6 coax cable, but I bought a new quad shielded coax cable to improve on that. System works great.