This is my set-up as well, with the addition of a Roku 3 (so many more channels than the TiVo) and a Mac mini as a media server for my own music and movies. I've had this set up for almost 2 years now, and it is working really well. I decided to get Netflix this summer (when all my regular network shows are on hiatus) to binge on their shows - Daredevil, Grace & Frankie, and just started Sense8. I think I'll be doing this next summer, as well. To round things out, I purchase a couple of shows from Vudu that I loved on cable (Major Crimes, Teen Wolf), but the vast majority of my television is OTA with TiVo. I'm totally spoiled by all these options and the way I can fast forward through commercials, or avoid them completely.
Unfortunately, no. That's why I have both; TiVo for all OTA info and recording and the Roku for all my streaming channels (Netflix, Vudu, Amazon Prime, Plex, Google Play, and even my local PBS channel). They work great as a team.