It does seem dubious, but I can see the argument that the government shouldn't be adjudicating which work resources are or aren't costly to allow. (Internal phone calls don't cost anything either, but I think it's fair to say union organizers shouldn't be allowed to ring up all the desk phones in an office asking them to support some labor action.)

That scenario is covered by the fact that organizing on company TIME is not allowed.

I think I disagree. This is exactly the role of the government to adjudicate. I would suggest a standard something like "everything is allowed, unless the company can prove significant harm". So instead of the gov saying "email is ok!" you just get to use email, and then the company has to go to the gov and prove that you using email is a drain on their resources in order to fire you.

Email servers, electricity, the time spent setting it all up, the server room that stores the machines, the IT department that maintains the machines and keeps things running, the client hardware that the employee interacts with...

You're explicitly allowed to put up signs in the break room, and the cost of the break room existing is DEFINITELY non-zero. Explain to me how those things are different? Email is the workplace.

The marginal cost of everything you mentioned is zero per email.

Essentialy zero isn't Zero at Amazon scale (or the scale of any large business)

Does an email server processing n emails per second require more power to process n+1 emails per second? My suspicion is that unless that +1 hits some capacity limit, the number of emails we're talking about required to organize union activities would be undetectable.

That said, even if it is detectible, I think that employees should be allowed to drain some small amount of a company's resources to organize. I am allowed to use company resources for emails like "who wants to go for beers after work?" why should I not be allowed to send "who wants to go organize collective action after work?"

There's still some drain from resources spent monitoring and stopping it. Even though you're already monitoring, you just end up with two cancelling out "essentially zeros."