I agree with Ken. The answer is a definite MAYBE. When the RCA STB first came out, it was basically proprietary to the RCA TV's. It had a non-standard scan rate, and a VGA output. Eventually a VGA to Component adapter was created. This still left the scan rate issue. Some people were able to make Service mode adjustment sets to account for this. Then RCA came up with a firmware upgrade which made it more compatible with other sets.
I believe the early Mitsubishi's had a proprietary connection and therefore have some issues. As Ken pointed out the Panasonic TV does 720p, therefore an STB that does 720p is a good idea.
Since many of the new boxes are essentially the same box, being made by the same company (Hughes), mixing and matching doesn't really matter if you buy the Toshiba, Mitsubishi or Hughes STB.