Is it common to caulk around the edges of vinyl tile instead of going underneath wood paneling?
Caulking from vinyl to quarter round isn't a very long-term solution.  The quarter round is small and flexible, the area is dirty, it sees a lot of traffic, it gets dirty.  The caulk will fail within a year or two of use and have to be scraped and redone.  Putting the flooring under the quarter round with no caulk is a much better solution.