The leak is on the top-most (whitest) nut, where it meets the base of the tank as shown in the below photo (with an additional photo for context).
Would I be able to just throw a ring of silicone sealant between the white nut and the tank base?
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To get the silicone to adhere you would have to stop the leak. This means you would have to drain the tank until there is no water to leak. A better approach would be to shut off the water, drain the tank, unscrew the water line connector, then unscrew the fill valve plastic nut. Then you can remove the fill valve. The problem is that it's tank seal/gasket is leaking. You need a new one, or a new fill valve (it comes with a new seal). Fill valves are cheap, so you're probably better off getting a new one.
Yes, you could seal between the tank and the nut. You'd have to drain the tank and have both parts dry. But there's a better solution that isn't any more difficult.
That nut is on the bottom of the fill valve column. Inside the tank there is a rubber washer between the base of the column and the tank. That's where your leak is. If the rubber washer has deteriorated, replace it. If you want to use silicone, do it there-- you can coat both sides of the washer to seal with the valve column base and the tank.
I did this before and it worked for me.