Hi Jim,
What a great idea! I know at least one owner who has had to replace the flooring because of water intrusion into the cabin floor and have been concerned about this myself. I have done quite a bit of custom woodwork (and caulking!) including some flooring work. However, I have not attempted to seal a floor edge in this way and have not done it in our boat yet,(though I may consider it this winter now that you suggest it!). I do, however, think it is possible if you (or someone you can hire) have adequate skills with a caulk gun. If you look in the "head" in your boat at the walls I think you will find the veneer is caulked around the edges with a matching color to the liner. The key would be to acquire a matching color of caulk to the liner color, with the appropriate flexibility and adhesion, and someone with the skill to lay it down. Maybe Richard Becker at RT can point you to the appropriate caulk.
If you do take this on yourself, I recommend you practice with some similar scrap material, the caulk product, and tools. Also, prior to laying the practice bead down make sure you have the appropriate solvent for the caulk. If you cannot lay it down directly with the gun satisfactorily you may be able to get good results by using a tool (an appropriate rounded edge like a spoon or even a finger!) dipped in solvent to form a consistent bead profile. After you can consistently create suitable results on the practice materials you should be good to go to apply your new skill to your new boat!