TV2 output
The short answer is yes, but with some precautions. Don't know why you would want to keep your cable subscription because you can get all of the local channels off of the Dish for an extra $5/month. The whole beauty of the TV2 output is to connect it to your internal cable wiring and see the output on ANY TV in the house without any adapters. Only stipulation is that you can move the TV2 remote to the room you want to view the TV2 output, but all TVs in the house will see what you have set either TV1 or TV2 to see.
Because the output of the 622 modulator (UHF), it might not mix well with another cable provided input. Technically, it might hetrodyne and cause all kinds of wierd signals on the channels. You may have to play around with the signal levels, but try this...Use a standard signal spliter and hook the cable input from the cable company on one input and the output of the 622 on the second. Then hook the output of the spliter to the cable input line. FYI, you would simply use your TV as before (Channels 2-13 for the basic cable) and then tune your TV to the UHF channel you set up on the 622 to see the Dish Network output. If you use a cable box, it is a little more involved, but since you indicated you have basic cable, and assuming you have a cable ready TV, it should work. I do not think you should hook up the output of the 622 directly in parallel with the cable company input. You could possibly damage the 622.