In the process of reflooring my covered porch with T&G ipe, I had to
remove the wood columns. The columns rest on the decking.

Question is whether to caulk where the columns meet the deck or not?
- Advantages:
Makes the joint look better and fills gaps
Keeps water out?
- Disadvantages:
Keeps water in?

One compromise would be to caulk along 3 sides, leaving the
"downstream" (i.e. pitched down) side uncaulked.

Any suggestions?

The columns are solid wood turnings with a 7x7 square base (integral
to the column itself) consisting of a solid 6x6 core and 1/2 facing
around the edges. I have restored them so that they are now in quite
excellent condition.