It's supposed to bring your hormone levels back to normal, and thus reduce acné, unwanted hair growth etc. It won't give you a cycle though - the bleeding you experience from the 21-day pill is just a "fake" period, induced by the hormone withdrawal, not an actual one. So basically, it won't cure PCOS, but it will lessen the symptoms that come with it.
With that being said, the pill does come with unwanted side effects that may or may not show themselves for you, so if it feels wrong, talk about it with your doctor and don't hesitate to change. There are two types of pills - "mini" ones that only have progesterone, or else combined (progesterone and oestrogen), and some might not work as well as others for your particular type of situation. And make sure to do blood work once a year at least to see if it impacts your cholesterol & triglyceride levels (it did for me).
Also, what I wish I had done before getting put on the pill was simply check my hormone levels. Like, it's pointless to do it when on the pill because your hormones are balanced artificially, but otherwise? It would've helped to see how bad things were or where I was at. So if you have the possibility to see an endocrinologist, you should probably go for it before starting treatment.
I was put on the pill as soon as I was diagnosed with PCOS, and the doctor kept saying "it's the only solution" etc. so I didn't really question it much. It didn't feel like I had any side effects, but it didn't really help either - I had to follow a 6-month Roaccutane (Isotretinoin) treatment to get rid of the acné. With that being said, I weighted about 100kg (220lbs), so my symptoms were no doubt worsened by the excess weight.
Now years later, I'm at 73kg (160lbs) for 1m75, which puts me in normal weight range. And yet, I did a routine blood test two weeks ago, and I have the cholesterol and triglyceride levels of a 50 year old obese diabetic - 2.97 g/l for the cholesterol when the norm is 1.60 to 2.20, and 2.56 g/l for triglycerides when the norm is 0.5 to 1.50. I tend to bruise excessively now, which never happened to me before. For instance, after playing volleyball for one hour, my forearms turn completely black and blue, when that shit never used to happen prior to taking the pill. And my knees get blue and bruised from sitting in seiza position.
And even with all this, the GP, gynaecologist, and dermatologist have all told me to "keep up the pill because PCOS", and dismissed my concerns about the blood tests and bruising as "just keep losing weight, duh". I already track my food compulsively, don't drink alcohol, don't eat fatty or sugary shit, no highly processed food, but it doesn't seem to matter to them. (I was at 67kg (147lbs) last year, but went to 73kg when I started exercising and building up muscle mass seriously).
Either way, I dropped the pill this week (I had been taking Yaz since August, and Cerazette prior to that), and I guess we'll see how it goes. As far as I've noticed though, the PCOS symptoms have been lessened way more by simply dropping weight and eating healthy than by the pill, so just keep that in mind.