As an ex-desk officer responsible for pre-boarding I can say that OOA certainly does lend weight but only if the home assessments are consistently supportive. Board officers aren't the idiots you might think, they smell a rat when a guy can't be bothered to get out of his pit at home but is an OOA hero when away.
Prom boards know about the "Halo" effect and will set aside those OOA reports that appear embellished (same goes for loan service reports) and the cut and paste variety (Theatre Cdrs are busy chaps after all).
On the other side of the coin, no OOA and you need a good excuse. In my experience the only guys who I ever heard complaining about the inequity of the system where those who weren't doing so well out of it and hoped that a few theatre medals might boost their chances of a leg up. Sorry guys but there is just too much genuine competion!