Can I use a coaxial cable as a DC power cable (without using it as a signal cable)?
Yes, this should work fine.  Even in its original application, the coax was probably carrying a DC bias to power the LNB on the satellite dish.

Assuming it's RG-6 cable, it should be good for at least 3 amps.

It's considered conventional to use the shield as ground and the core as +V, though it doesn't particularly matter from a functional point of view.