I can't imagine any reason why they would since it's a dissolved gas and not a solid, plus if the outflow is placed near the surface you'll be creating enough agitation for gas exchange. What type of media are you worried about?
There wouldn't seem for there to be any place for the oxygen to go. However, just having a canister filter can lower the oxygen levels in the water, since it's possible to orient the return to prevent surface agitation, which decreases gas exchange.
Not directly. If anything, they increase redox by polishing the water. As authemal stated, they can potentially prevent surface oxygenation if no other means of aeration/surface agitation is incorporated. This may or may not even be an issue depending on the specific O2 demands of the tank in question.