I can see water being sprinkled over the lever by children and collecting around the faucet, but I wonder whether there is as much water precisely going down that hole as when you poured it.

One way you could deal with it is to tape a small cup in the cabinet - such as a plastic butter or yogurt container - below the opening and catch the water. (Not the solution you are asking for, I know. I will keep thinking about this.)

I just poured a little water down ours (which is on the back of the faucet) and it ran down the connection under the sink as well. Maybe you can put some silicone around it. But, like Graywings said above, the bit of water that accidentally gets onto it is not going to be as troublesome as pouring water over it.

All my faucets have the lever in back and I've never had any damage to my cabinets from water leaking down the lever. I think it's highly unlikely that anyone will be reaching that far back with wet hands to turn the water on and off and if someone decided to use the lever, they probably have dried their hands before they reached back to open the stopper for drainage.

From my observation, kids tend to just grab the edge of the handle when using that type of handle. Plus, the design of the faucet handle allows any water droplets to drain back toward the sink.