GPS over 75 Ohm Satellite Cable

I needed to get a GPS signal for a couple of upcoming projects that use it for time synchronisation. The problem? Where I intend to place this equipment happens to be a windowless cupboard in the middle of the flat, and the metal roof blocks out the GPS signal. 

However! The original builders ran satellite coax cable to each of the bedrooms and the living room and terminates in said cupboard, along with two feeds from the communal Satellite distribution, allowing you to "patch" services as you require. I'm curious how many residents have discovered this as its all hidden behind a blank face plate, but it has previously came in handy when I wanted to mirror the Satellite reciever to the bedroom and ended up with a rather hacky, HDMI over Ethernet over Coax solution with cheap boxes from China that effectively ran powerline over the Coax cable.

But GPS receivers are expecting 50 ohm coax, not the 75 ohm cable used for television distribution. Will it work?