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Technically she can, esrb never rates online gameplay itself. (wonder why)
But we all know there is always a bunch of swearing, insults everywhere, and occasional racial remarks in COD, and more than likely people trying to produce offensive/obscene images with their emblems in BO2. (most of this done by none other than other kids)
If you are ok with that than by all means let her play, but do show how to mute/report people.
Common sense seems to be more uncommon. Occupy Sesame Street