Depends. In some areas they do what's called simulcasting, which means all the analog stations actually have a digital equivalent and the TiVo will record those just fine. However it can not record any channels that are analog only. In my area we have Charter and we still have about 30 analog only channels. I can't record any of them on my 4 tuner Premiere.
The easiest way to tell if you have any analog channels is to go into Messages & Setting, CableCards & devices, Tuning Adapter, Test channels. Any channel you can not access on this screen is analog and will not be capable of being recorded on a 4 tuner unit. If all of your channels come through this screen then you're fine.
Developer for VideoReDo