Satellites are not impossible on a Flat Earth. They could circle above the disc, around the North Pole, exactly the same as the Sun and Moon.
By whatever system is accepted to keep the celestial system rotating in the particular model, possibly. Unless they accept that there is something preventing anything from going high enough or that the celestial bodies are not physical.
Since space agencies are full of lies, it's entirely possible that they operate satellites, while still lying about how they work.
Though people can launch cubesats themselves without appealing to space agencies, so there could be nothing much to hide. I am not sure how easy it is, but Keplar's laws of orbit are recommended to take into account when launching it.
If anything, it raises many more problems... The number of people in on the conspiration goes way up ; satellite based technology is readily accessible and testable by individuals ; much of today's information would not exist without them (starting with weather forecast) ; etc.
They would work by Keplar's laws, which are based on the Round Earth, so either these laws match the FE way of orbit (like with some whirlpool circling above), or is a lie of some sort. Another thing to remember is that with things like ISS and cameras on satellites, you see apparent curvature and Zero-G, which you may say is faked, but if allowed, would have to be explained.
It would be absolutely easier for FEers to accept satellites and just adapt them to FET, as they do with seasons and eclipses for example.
The sun and moon would be satellites, what you are talking about is artificial satellites launched, which some do accept. I wouldn't have an issue with it, but I am neo-planarist anyways, so...
Still, it seems to be one of the few points that most FEers agree on. So I would like to see what it accomplishes. How is this point useful in FET ?
I would prefer a model which can adequately explain how satellites launched are able to be sustained circling the Earth. It could be good for FE.