The answer is no, a satellite TV system operates on a different radio frequency than that of a Wi-Fi or any wireless local area network system. There is no reason why these signals could interfere with each other.
For instance, a Dish Network satellite signal operates at C-band ranges, which is between 4 and 8 GHz, or the Ku-band range, between 12 and 18 GHz. A Wi-Fi system operates at S-band frequencies of 2.4 to 5 GHz.
Furthermore, a Dish Network satellite signal is in electromagnetic or radio form only until it is reaches the LNB, after which it is converted to electrical signal. When it goes inside the house (which is usually the case), the signal is already in an electrical form that shouldn't interfere with any Wi-Fi signal.
Now, there are a lot of things that can interfere with a Wi-Fi signal, or at least dampen it to render feeble enough. Then next thing you know, your internet becomes too slow or worse, no connection at all.
Common household devices that emit radio waves can be suspect to interference with your Wi-Fi system. Cordless telephones, baby monitors, car alarms, microwave ovens, even bluetooth devices that are used on gaming consoles are suspect to Wi-Fi interference. There are ways to resolve this, some simple and some as complicated as shifting to an altogether different product, such as using wired phones instead of wireless phones, or using DECT wireless phones that uses different frequency ranges. For some devices, you may need to simply relocate the offending device or else the Wi-Fi modem.
Also, you should consider the Wi-Fi network itself. Usually, Wi-Fi signals can travel for about 100 feet or 30.5 meters, after which you will range extenders or repeaters to increase the router's range. Physical barriers such as walls and doors can block the signal, so account for all these too.
Lastly, a Wi-Fi signal is susceptible to a rain fade, just like a satellite dish setup. Water is an excellent absorber of radio signals, so you may expect a degradation of signal strength during heavy snow falls, rains or storm.