There is no such thing as 'pixel skipping' in first person shooters.
Pixel skipping only exists for 2D mouse pointers such as the windows desktop pointer. In that case if you lower the screen resolution, you reduce the density of states that the pointer can occupy, and thus reduce the available precision for pointing at stuff. Pixels are macroscopic states - you want to be able to point at each one, so skipping over pixels is bad.
However in 3D games where the mouse controls rotation, the rotations are performed in degrees, not pixels. It doesn't matter whether you are using a 1080p or a 1x1 pixel blob, the game will respond in exactly the same way to your input. The mouse input code doesn't even know or care about what is on your screen.
So the screen resolution only affects the visual detail of the player's view of the world, not his control of it.
You *can* use the screen resolution as a basis for estimating how much mouse dpi is 'useful' for your setup - this is something that both Sujoy and myself have formulated in the past. But these estimations are not magic numbers and you certainly shouldn't lower the quality of your setup to try and match these estimations. They are useful for debunking the gaming mice "you need 9000dpi to be pro" myth in a quantitative fashion.
tl;dr: "pixel skipping" is not a valid reason for deliberately choosing a low resolution over a high one in 3D games. The precision of control is unaffected, only the visual detail changes.
Lately razer advertised their latest deathadder as native over 9000 dpi sensor...
Heartless, will you change sensitivity/setup any for quake chapions?