As a cat lover, I can't go along with bobechs' suggestion. But points for thinking outside the box, I suppose!😀
I believe you have tar paper under your siding based on your description. Not a vapor barrier, as you say, but it prevents water that makes it past the siding from getting any further into the wall. Theoretically, you could seal the tar paper to the foundation with foam spray/caulking/something similar. Until someone with more siding and air sealing experience joins in, my thoughts would be around how to determine if this is really going to help much or are there other things you can do that would bring a greater return on your efforts. If there aren't large gaps, perhaps focusing on attic insulation, air sealing around doors and windows, etc may more effective.
Later on if you replace the siding you can put on a vapor barrier, seal holes, add rigid insulation and at that point, perhaps seal around the cladding where it meets up to the foundation if you decide to as part of the project.
Sorry not to be of more help but I've never heard of anyone considering what you've suggested except to repair holes from rodent or insect intrusion and that was in a spot by spot effort, not around the entire perimeter.