It won't tell you anything. The synthetic progesterone (progestin) mimics your natural progesterone, which is what makes your temperature elevated after ovulation. So even if you do ovulate on the BCP, it won't be revealed by temperatures because of the synthetic progesterone.
Secondly, the BCP shrivels up the parts of your cervix where fertile mucus is produced, so you won't have a reliable CM pattern to go by either if ovulation does occur. The cervix is very delicate and can take a long time to recover from this effect.
You do know that the BCP doesn't regulate PCOS right? It just covers up the problem for a few months and then your body has to sort itself out again after you stop (it's a lot of hormonal chaos on top of the chaos that's already there from PCOS). It's much more helpful to actually treat the PCOS rather than covering it up for a few months. Longer cycles are not actually an impediment to TTC, it's just a matter of being able to identify ovulation so you don't miss your opportunity. I have PCOS too. We've conceived as a result of ovulation on CD23, CD58, CD50, and CD38.