Ammo may or may not be airtight.
Even if not, an oxygen absorber would have no impact on the efficacy of smokeless powders. Neither nitrocellulose nor nitroglycerin out-gas, and even if they did, propellants do not rely on gasses within the case. I'm at a loss, however, as to why you want to store ammo in an oxygen-free environment. I get the feeling that you haven't thought this plan all the way through.
What you need to be concerned about is not gaseous oxygen, but rather moisture and temperature extremes.