You're a little confused on the Roamio's capabilities. There is a Hulu+ app on the Roamio, which you can use to access your Hulu+ account and view shows. You cannot record Hulu+, or any web-delivered content. Despite the fact that plugging the Chromecast into the Tivo most likely won't work at all, even if it did, you could only watch web content, not record it.
A Tivo records Cable or Digital Antenna TV signals only. It can access many other services like Hulu+, Netflix, Youtube, etc, but not record those.