Yes, there is a potential advantage. Connecting the ends of the stiffeners will add a bit of stiffness to the skin. This has two effects, one if there is any oil canning, it will lessen the likelihood of cracking at the rivet nearest the TE. Apparently this was found on the early RV6, but none widely reported on the riveted TE style rudder. Second, it will add some torsional stiffness and help add some margin to Vne. No quantification on either.
So, it is a good idea. Just don't add a huge glob on each rib, just enough to contact both sides. Be sure to balance your elevators separately, before flight, and after paint.