The hole itself isn't that big...size of a silver dollar, maybe? but the thing is, the entire area under the base plate will be all corroded...possibly to the point of having pin-holes in it.
have you seen Rich Luhr's "Vintage Thunder" restoration blog? He had pictures that showed this in detail.
After removing the antenna, I sanded down all the corrosion with a wire brush...which leaves the spot looking rather nasty, (but I hope removing the corrosion will be like removing a cancer, and stop further deterioration.). I cut a patch out of a piece of aluminum that I picked up at HD, using the antenna base plate as a stencil. traced around it and marked the holes with a sharpie...cut/drilled, squished it on the roof into a bead of vulkem, and riveted it in place w/ olympics. Looks great...but you'll only see it if you're 9' tall.
now, the corrosion on my roof wasn't as bad as on Vintage Thunder, but it still looked like crap. The skin itself wasn't leaking; it was coming in right down the crank shaft of the antenna. I though I might be able to repair it, at first, but when I got it out, I found the innards to be so heavily rusted that they were just frozen. too far gone. No parts (o-rings?) are available for it, so anything done would have had to be improvised...I decided it just wasn't worth it.
Maybe if you can get the handle off the shaft on the inside, you can get a finger up in there and feel around and find out if there's water getting in there. When water comes down around the shaft, it hits the insulation, and wicks off every which way. I only saw water dripping from the antenna handle during heavy heavy rain. And even then, I didn't **know** that the water was getting through the roof there; it could have been coming in somewhere else, (nearby vents) and just finding its way into the interior of the trailer through that hole. can't tell for certain without dropping the ceiling.