I also had FIOS Internet installed for over a year before TV service. With Internet service, I just had an ethernet cable coming from the ONT to my Actiontec router. When FIOS TV was installed, the tech unhooked the comcast feed and connected the coax directly to the ONT. That was sufficient to give all my televisions the full range of digital channels.
However, in order to receive the advanced features of FIOS TV, including the interactive guide, video-on-demand, and the Media Network DVR, the tech had to run a separate coax line from the ONT to my Actiontec router. So now I have both coax and ethernet cables connected between the ONT and router. The rest of my house coax wiring did not require modification.
The tech originally thought that the advanced TV features would work without the coax cable to the router, but he wasn't able to get it to work that way. I suspect that the ethernet cable is superfluous now, but I haven't tried disconnecting it.