Can I Still Watch Television If My Other TV Is An HDTV?

This is kind of a complex question that needs the easiest answer possible. I will start from the beginning. There are two regular (SD) TV's in the household (one in my room and one in the front room) and they use DISH Network's dual receiver thing where one receiver box sends a signal to both TV's but the two TV's can get their own programming. If I upgrade to HDTV through DISH Network for my TV, will the other TV still receive the signal? To rephrase it, if I had HD programming going to both TV's, would there still be a picture on the regular TV? Also, do I have to pair an HDTV with an HD Receiver or would an HD Receiver work with an SDTV?