Google doesn’t want its employees organizing. Why? One of the most crucial things about organizing is being able to contact your fellow employees. Yes the equipment is Google’s, but also I would contend that conversing with your fellow employees is in service to the company, in service of making the company better.
If I am trying to organize I would just send a blast asking everyone to add their personal emails to list. Could google call that organizing and penalize? What if I just wanted a personal email so I could schedule getting a beer.