You can use your SD dvr and HD reciever on the same TV. I don't believe you can connect them together(receivers). The HR20 is dual tuner and records SD as well as HD. And yes, it's a good idea to keep the SDdvr as a backup for the HR20.
Edit: If you get a new reciever, you could use the new remote control to control both the HD reciever and the Tivo.
Edit: If you get a new reciever, you could use the new remote control to control both the HD reciever and the Tivo.