I wonder if it might be that the pill "corrects" the hormone imbalance that we get with PCOS, so actually makes you more likely to conceive while the pill chemicals are still in your system?
No, if anything the pill masks the symptoms of the underlying hormonal problem that has always been there. Also the causes of PCOS are still not fully understood.
PCOS is a very individualistic disorder and affects each woman with it very differently. The commonality though is the cystic follicles on the ovaries. These do disappear - only to be replaced by further cystic follicles. Some of these follicles pump out hormones further disrupting ovulation (that is also why OPKs are of no real use in women with PCOS), some are dormant and others may contain an egg. Some women with PCOS do ovulate occasionally and spontaneously as well BUT most will need some more help in order to conceive.
If your Day 2 test shows the LH/FSH imbalance (i.e excess LH level compared to that of FSH) then it is likely that your Day 21 will also show no ovulation as well. In my particular case my sky high LH level put me at greater risk of miscarrying. LH and FSH are two very important hormones as they kickstart the ovulation process.
Would not place too much emphasis on temp charting particularly if you end up with a very difficult to interpret chart. Many gynaes as well do not take much notice of such charts primarily because they can be unreliable. I would go by the ultrasounds and blood test results rather than a single positive OPK result as these are far more accurate. Also using OPKs every day can cause you yet more stress in an already difficult situation,
Not every women with PCOS is actually insulin resistant (yet another conumdrum) so you may or may not be prescribed Metformin by a consultant gynae or be given a met/clomid combination (this can work well for PCOSers rather than just clomid solely).
If your periods are really irregular as well, the tests can be done according to calendar days (i.e the 2nd and around the 21st of the month). These tests should be repeated and you should have regular internal ultrasounds to further assess the state of your ovaries and uterine cavity (lining can be very thin in PCOSers).
HSG test is a tubal x-ray. It is a useful test to have done as it can give information not usually accessible by other methods. Deformities INSIDE the tube can only be seen on a HSG. It should not hurt providing the dye is injected both slowly and carefully. The staff should give you a couple of painkillers beforehand. If you have a HSG sanitary protection should be used post proceudre as that dye (only about a teaspoonful is used) comes out!.
If you are not already under the care of a gynae at a subfertility unit you should be. Some GPs are pretty much hopeless when it comes to PCOS and many such cases require careful management.
Try and remain within the correct weight range for your height; PCOS symptoms can be worsened by excess pounds. Many women find a low GI/GL eating plan helpful as this is more sustainable to do longer term than say low carb.