Your support post should be on top of post bases, which are metal or hard plastic and raise the wood off the concrete to prevent wicking. If yours are, as I can't see because of that plant, then NO caulking. The area must allow for water to run away to keep it dry.

 

If it's lasted 50 years the way it is, why do anything?
If it is sitting right on the slab with no post block the last thing I'd want to see is any form of caulking!