Can I get OTA through basic cable?

I just upgraded from a Series 2 to a Premiere with an antenna input. I have basic cable that supplies OTA HD channels to my tv. Tivo folks told me that I have to connect an antenna if I want the Premiere to get the HD channels.

So I'm wondering, if my basic cable has the OTA channels, can I attach a splitter and plug my cable into the antenna input? Would the tivo box recognize the channels?