RG-59 OK for new install?

I have Cox phone service, and I'm considering adding Advanced TV Ultimate and whole-home DVR.  My house was pre-wired for cable TV when it was built, and there is a feed near the current telephone modem so hooking up to the TVs in the house would be easy. But the house was built 35+ years ago and the cable is all RG-59/U.  Will Cox install the TV service with that cable?