My thoughts on the three options: Nothing, Varnish, and Glue.
If you rely on friction, you better hope that the furniture will always live in a moist environment. As the wood dries, the wood will shrink and the plug will fall out. Maybe not today, but at some point, it will just fall out.
Varnish works as a weak adhesive, but more as a luting agent which simply fills any air pockets and holds the plug in with suction. This method is the equivalent of licking a playing card to hold it to your forehead. Yes, it is “glued” but it is not permanent. If you need to access the screw below, you just pop it out and get straight to the screw.
Wood glue is the last option and offers the most secure method of holding it since it will be glued in just like all the other pieces of wood in the furniture. This means that the plug will never come out but it also means that if you need access to the screw, you are going to regret having used glue!
Since this is my very first time using wood plugs, I was concerned that I might have messed something up and might need to gain access to the screws to remove or relocate the strips of wood. If for any reason I need access, I don’t want to destroy everything just to get to the screws, so I chose varnish.
I also cut out some extra plugs so that if I like how it all is working, and if the plugs fall out and are lost, I can replace them with new plugs and with wood glue. I just have issue with permanent things, so the retrieve-ability of the plug with varnish really appealed to me. Once I know that I like the furniture there on the deck like it is, I will consider replacing the varnish with wood glue, but for my first attempt at plugs, I wouldn’t want to bury my comfort in permanent glue.