Should I remove the gasket, put the silicone grease on, and replace, or can I just put the grease on the gasket while it's in place? If it's the latter I'll have to get a tool to get the gasket out.
Depends on which gasket, watchdoc. (And the watch I suppose) But on Rolex replicas for example, what I do is remove the gasket from the case back (Case back tool required), it just pops out, and coat it in silicon grease, then reinstall the gasket in the groove. I remove the stem (Case back tool and small jewelers screw driver required to remove the stem) , and use a small brush to apply grease to the gasket in the crown that seats onto the tube, I also apply grease to the gasket inside the tube and the one on the tube. That said, I can see where it would be better to remove all the gaskets and grease them before inserting them to insure that ll sides of the gaskets have grease.
The crown barrel (where the winding stem screws into) on a rolex triploc will seat inside the tube gasket sealing it there while the gasket in the crown seats to the top of the tube, and the little gasket on the outside of the tube seats inside the crown.
I also grease the threads too, helps the crown screw down with less friction and adds just that much more grease to serve as a barrier agaist water intrusion.