Obviously this is very statistical. Basically I'm looking for an order of magnitude. One geostationary satellite would cause a pinball effect or would it be more like 10 satellites?
I'm concerned there will be a war before we have a self sustaining Mars base.
At geosynchronous altitude there aren't enough satellites or varied orbits to create an impassable debris field. Consider that the sphere surrounding Earth at an altitude of 36,000 km is huge. Deconstructing every geosynchronous satellite (including graveyard orbits) and spreading them across this area in varied orbits would not even begin to constitute an impassable barrier. Add to this the fact that most satellites at this altitude reside at 0 degree inclination and the resulting debris would in reality occupy an equatorial band.
I'm not even sure that a Kessler syndrome type scenario at LEO would pose much of an issue for deep space travel. Some orbits would be especially dangerous, but the average debris field would still be sparse.
Photos such as the one below (ripped from wikipedia) make it seem like a debris field would be impassible only because they magnify the size of the mapped objects (otherwise you wouldn't see anything):
The main danger of these scenarios is they make orbits unusable until the debris are removed or their orbits decay. For GEO, the time for orbits to decay is essentially forever (as far as we are concerned). Unless I am mistaken (and if I am someone please tell me why), the idea of a Kessler syndrome event preventing deep space travel is mostly hype.
Despite how it's often dramatized, creating a debris field so large it's impossible for us to even get to outer space would require an absolutely enormous amount of satellites; far, far more than we would ever need to operate (or would even be logistically possible to operate), especially for the specific purpose of spying.
The main risk with Kessler Syndrome is that "popular" orbits with a lot of satellites could become too dangerous for other satellites to use. Since we already track debris and plan launches and maneuvers accordingly, it's possible to design the moon/mars mission to simply avoid such areas, similar to how the trajectory of Apollo's lunar transfer was designed to skirt around the strongest part of the Van Allen belts.
Worry not: Even if we sent up enough spy satellites for your fear to be realized, the warring nations would have very strong strategic interests in figuring out how to clean the debris so they can replace their spy satellites as soon as possible. Very little motivates humans as much as war effort.
