No, it only records from cable. It has video inputs but as far as I can tell they are completely inactive.
If you want to record from DirecTV, just replace your Sony box with a DirecTivo for $99 + $5/month. Guess whether it's worth it depends on how much you watch NFL Sunday ticket.
I would not go with standalone Tivo with your setup. You wouldn't be able to record in high def, and can only record one thing at a time. Get both Comcast DVR & DirecTV DVR, or just Comcast DVR & give up on recording DirecTV.