I hate to say this, but the facial hair won't diminish when you lose weight. Once one of those pesky hair follicles has set up camp on your chin/neck, etc., it's there to stay, unless you get it zapped by electrolysis or laser. Though on the upside, once you've lost the weight, new ones hopefully won't form so readily.
I've never had PCOS officially diagnosed, but do suspect I have it--I've certainly had problems with facial hair (and not just facial hair,sigh) and other period/weight problems that certainly fit the diagnosis. Luckily I didn't have trouble conceiving my DS, largely, I suspect to the fact I'd just come off the pill when we started trying.
I think the reason a low carb diet is recommended for PCOS is something to do with the link with insulin resistance. Some folks find their symptoms improve when taking metformin, which is actually a drug for use in diabetes. But on low carb, you aren't producing so much insulin anyway, and you don't get the highs and lows of insulin you'd get when eating an ordinary carb-laden diet.
It's all fascinating stuff... When I did Atkins a couple of years ago, my periods became more regular than they'd ever been--and for some reason, they've stayed that way.