The answer is no, a satellite TV system operates on a different radio frequency than Wi-Fi or any wireless local area network system. There is no reason why these signals can interfere with each other.
For example, a Dish Network satellite signal operates in the C-band ranges, which is between 4 and 8 GHz, or in the Ku-band range, between 12 and 18 GHz. A Wi-Fi system operates in the S-band frequencies. 2.4 to 5 GHz.
Also, a Dish Network satellite signal is in electromagnetic or radio form only until it reaches the LNB, after which it is converted to electrical signal. When you enter the house (which is often the case), the signal is already in electrical form which shouldn’t interfere with any Wi-Fi signal.
Now, there are many things that can interfere with a Wi-Fi signal, or at least muffle it to weaken it enough. Then the next thing you know is that your internet becomes too slow or worse, there is no connection at all.
Common household devices that emit radio waves can be suspected of interfering with your Wi-Fi system. Cordless phones, baby monitors, car alarms, microwave ovens, and even bluetooth devices used in game consoles are suspected of Wi-Fi interference. There are ways to solve this, some simple and others as complicated as switching to a completely different product, such as using corded phones instead of cordless phones or using DECT cordless phones that use different frequency ranges. For some devices, you may need to simply relocate the offending device or Wi-Fi modem.
Also, you need to consider the Wi-Fi network itself. Typically, Wi-Fi signals can travel approximately 100 feet or 30.5 meters, after which, you will extend the range of extenders or repeaters to increase the range of the router. Physical barriers, such as walls and doors, can block the signal, so keep all of these in mind as well.
Lastly, a Wi-Fi signal is susceptible to rain fading, just like a satellite dish setup. Water is an excellent absorber of radio signals, so you can expect signal strength degradation during heavy snowfall, rain, or storms.