I guess now I could hit each screw head with a dab of silicone.
Larry,
After trimming off the excess putty tape, it is wise to run a (small) bead of sealant around the edges to protect the putty from drying out from being exposed to the elements, and to form a second barrier.
Applying a dab of sealant on the screw heads is a good idea, but a method that assures a better chance of no leaks is to remove the screws a couple at a time, inject sealer into the hole, then reinstall the screws.
The reason for the dab of sealer on the screw heads is to prevent water from following the screw threads into the wood.
By injecting sealer and reinstalling the screws, you have created a gasket/seal that won't allow any moisture to follow the threads, even if the screw head to flange area opens up.
Rob