They certainly could if the TV is connected to your receiver, but not if the connection between your TV and receiver is disconnected.
If your satellite system is AT&T Direct TV, then their boxes are real junk, and have internal ground loops. But if there is no connection between that system and your receiver then will be NO hum, until you connect it up.
The other issue with satellite systems, is that there must be a grounding block going up to the dish, with it own ground. That is code, for lightning protection. However, unless you are really obsessional an bind that to your panel as well, with a massive cable, you will have a ground loop.
Basically satellite systems are a nightmare, and unless you really know what you are doing, will definitely give you a buzz!
You can not use ground isolators with satellite systems either, as the dish is phantom powered, and an isolator cuts the power to the receiver at the dish.
I went through all this at our former lake home. If you are into HT, satellite systems should be an absolute last resort.