It's certainly no problem to use existing cable to distribute programming from your receiver throughout the house. At the very worst, you might have to add an amplifier at the RF output before you split it off to the various rooms (if you had a ton of TV sets hooked up).
But, the biggest problem is...everyone would have to watch the same channel on the sat receiver! Because there is voltage across the coax line between the dish and the receiver (used to power and control the LNB), there's no easy way to run different receivers at different locations all sharing the same
coaxial cable going to the LNB. Signal levels aside, the individual receivers would have to watch the same satellite (and same polarity transponders), and one receiver would have control of the LNB and all others would have to be DC-blocked, meaning they could not control the LNB.
Now, if you had a lot of money and time (and were just plain nuts), you
could set up a bank of
satellite receivers, each of which feeds an RF
modulator on a different channel, with the whole mess feeding the cable. But, then you've just re-invented cable television!
