Would the phrase read "Run, Joey, run!"...or does the placement of the vocative commas make absolutely no sense?
One of the most famous lines in English movies is from Forrest Gump:
Run, Forrest! Run!
but I don't think it's a problem (and I have often seen it written so) to write it as a single sentence:
Run, Forrest, run!
(Forrest is, like Joey, a given name).