Are we discussing hypothetical scenarios or are you thinking of actually trying it?
From my perspective, trying to be rebellious for no good reason is a waste of your effort and time and doesn't do you any favors in the long run. You can wear adidas shoes if you decide to run in your treadmill at home or something. At Nike HQ it's a bad idea.
It was (probably) your choice to work for them and they will pay for your salary. We all know that it wouldn't make a bit of difference on their sales if you wore any other brand other than Nike. But the board and high staff must promote their brand in any way they can and what good would be for their brand credibility to allow their employees to wear their rival's merchandise? Along with that "being part of something bigger" brainwash bs.
I have sneakers of both brands, I don't own anything to them. My money, my choice at that moment. If they provide you with free merchandise (they will) at least try to act grateful.
Put more simply, if you really want to wear Adidas to begin with, why not apply to them in the first place? They are stronger in Europe, but I'd be surprised if they don't sell well in U.S as well. Or will your rebellious persona think of wearing some Nike Pegasus there too?