Running coax through a UPS

I have just purchased a new iMac and am planning on picking up an APS UPS. I am concerned about a power spike coming in through the coax. Does anyone here run their coax through a UPS before their modem? If so, do you notice any change in your signal? Is this something I even need to worry about?

What's the coax for? I have a surge protector that I can plug the phone line into to protect from lightning strikes, I never had any problems using it. If it's designed for it then it'll be fine.

The coax runs to the cable modem for internet access.

And then one would assume an Ethernet cable runs from the modem to the Mac, correct?

Can you get a power surge through an Ethernet cable?

Yes, correct. I'm just wondering if I protect the mac by plugging the power cord into the UPS, am I still vulnerable to a power surge through the coax/ethernet?

I think the coax might be grounded as it comes into my house...in which case I may be OK.

Can you run the router/modem off the UPS too? If so, spikes would never reach the Ethernet.

Edit: Oh wait, so you're worried about spikes getting in through the coax? I doubt it, a lightning strike might possibly affect it slightly, but mains electricty won't get in unless someone at the other end makes a really serious mistake.