It's possible to do about anything you want to do, since it's your boat. However, possible doesn't always mean it's the right thing to do. You've not only got to consider that you're creating another opportunity for water intrusion, but then you will have the "how are you going to secure the wire up the mast" issue to deal with. They VHF doesn't have to be on top of the mast, ftr.
Sounds like a good time to get a Bosun's chair, have a couple of friends over for "beer" (not provided until after the task is complete of course) and take a trip up the mast. It's always a good idea to inspect all things atop there anyway.