Singa I don't think you'd have an LH surge if you don't ovulate (ie if no egg is released). From what I understand, we are born with millions of eggs. Each month, thanks to the right combination of hormones, a few eggs mature, each in their own follicle, until one reaches full maturation and is released from the ovary (ovulation). In women with PCOS, we don't have the right hormone levels to get those eggs to full maturity and release, so the eggs grow a bit and then just sit there in enlarged follicles. These are the 'cysts'.
I have PCOS (absent periods, acne and cysts). One doctor told me that fertility drugs wouldn't work and said I'd have to have IVF. the next doc put me on Metformin and I started having a 3 monthly cycle. Then I got pregnant after 3 rounds of clomid. So there is hope!
Here's some info I found helpful