If there are gaps where dirt has contaminated the wood so the clear caulking will not stick you may have a mess, later. The caulking may skin over in an hour or less, but may not cure enough to walk over for a while. The caulking should be coated with the water-based finish after it has hardened so everything has the same gloss level. The caulking is going to shrink a little when it has cured and will not sand easily. You still need to apply at least three coats of finish in a kitchen. I prefer to use a two part finish so it is more solvent resistant and tougher. It is more expensive, but with all the labor investment I want it to last. It's a lot of work to tear out and replace. If you experiment with these materials so you are confident, you will be getting extra use from what you have. Be sure to let any stain dry well. Oil stains will help seal the wood and any dirt between the boards. The stain between the boards will take an extra long time to cure enough for the caulking to stick.
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