As a FAA controller, and a NATCA representative, I can tell you that in today's environment, it is NOT adviseable to ask for forgiveness afterwards.
As far as having the equipment in the building, I doubt very seriously that this would be allowed. While some NATCA locals have been able to get wireless networks set up, the usual answer today is "No." In fact, some locals are being told to remove their high speed internet connections totally, even if they are buying it from an outside source. The stated reason is that the FAA doesn't want to have an outside company's equipment in the building for security reasons. however, most feel that this is the FAA's way of making a local deal with dial-up service, just to make things more difficult for the local.
Yes, one can always ask. The worst answer they can give is no. And if they say yes, then great. Personally, I don't see a problem with passive equipment like this.
But I would not recommend installing any kind of electronic equipment without permission. To many good people are getting fired over the most idiotic stuff these days.