It’s Amazon’s internal network, and Amazon’s email system, so they have the full right to control what happens on their resources.
At the same time, I find that deleting the an email after it has been sent by the sender unknown to the sender to be a kind of gaslighting, and dystopian. Having a policy to not organize using work resources might be harsh, but at least it is more transparent as in the proverbial line is drawn in the proverbial sand.
I personally think email is equivalent to an office bulletin board. What NLRB has said about that is you simply can't be DISCRIMINATORY on non-work issues. So if you can post on a bulletin board about sponsoring you in a Charity Fun Run, then you can post about union activity. If the employer only allows work-related things, then it's fine for them to not allow union activity.