Can I use MoCA to connect my older TiVo (Series3 or Series2) to my MoCA network?

Yes, but it's probably not necessary. Older TiVo DVRs (Series3 and Series2) don't allow you to stream shows from other DVRs or use TiVo Stream, so a wireless or powerline connection is generally good enough to use. However, if you find transferring shows is too slow on your current network, you can upgrade to a MoCA connection. You would just need to use a TiVo Bridge (available in the TiVo store) to connect each Series3 or Series2 DVR to your MoCA network. Get detailed instructions here.