Having taken apart pocket hole plywood, I can say that the glue added a surprising amount of strength (raw wood, not finished). So glue clearly adds strength to the joint so I always use it (because I can). I have only used pre-finished plywood a few times and I used glue when I would have raw edges touching (like in a dado).

I do not hold a lot of hope that my regular glue will hold to the finish. If I really needed the strength, I would at a minimum scuff the surface and I would probably perform a few tests. To convince myself that I was happy with the strength. I would trust E6000 to hold, but that really is not suitable for this application I don't think.

Jim Becker mentioned using a jig to sand right along the edge. I suppose that you could do similar with a router table and do more than scuff the finish.