These are all simple integer calculations and for a modern computer is nothing. Some modern games have even gone as far as simulating the trajectory of every bullet (ARMA 2), meaning every bullet arcs and takes time to reach its target. Even that is nothing because typically a player will only have at most maybe 3-5 bullets in the air at once, so with 100 players there might be a few hundred bullets in the air. So that's a few hundred simple integer calculations every frame to update their trajectory/position.
To put that into perspective, a scene in a modern game can have millions of polygons, each with a texture that has dozens or hundreds of pixels. The reason most FPS games don't support that many players is because if all those players end up in the same area it can cause a lot of slowdowns on the clients, since then your pc has to draw like 50 players at once. Plus, for a typical competitive FPS like battlefield, COD, TF2, etc. there's no point in having that many players. It doesn't make those games more fun, in the same way that having 100 players in a football game wouldn't make it more fun.
Wrong. Absolutely nothing in 3d is done with "simple integer calculations". Anyone that has a clue knows that everything in 3d graphics is done minimally in floating point, with emphasis on precision/speed in terms of tradeoffs.
Let's take your assumption and run with it for a minute though.
A "couple hundred" players = 200 player hitboxes.
3-5 bullets each (4 average) * 200 players = 800 bullet hitboxes + 200 player hitboxes + an undefined amount of "terrain" hitboxes.
60 frames per second (being generous) = roughly 16 milliseconds to calculate polygon movement, calculate hit tests, register hits, then update all 200 players and 800 bullets each frame. Hit testing is a very expensive calculation, and while there appears to be only about 1000 items to check (which is very manageable in 16ms), that doesn't take into account hit testing the various terrain and other obstructions that can get in the way.
This is just a very, VERY minimal example that doesn't include dozens of other things that happen behind the scenes as well. Not sure about you, but I can't tell you the last time I've been on a server that was even NEAR 16ms in latency IN ONE DIRECTION. Add in player reactions, movements, new bullets, this, that and the kitchen sink, along with the fact that
most players will be averaging roughly 150ms round trip actual latency, and you can see this formula simply won't hold without some very creative optimization.
Polygon counts are far more manageable through LOD, culling and other optimizations. In fact, polygon counts are basically irrelevant in modern gaming, unless you have developers that simply don't know or understand how to optimize for these things *cough*Crytek*cough*. Polygon count simply has absolutely no bearing on the network latency or bandwidth, nor does it have any bearing on server-side processing of the data that needs to be processed.