The TRUTH is, it is hard to predict (what will happen if birth control fails) among various people. Some do better than others with birth control. I know of several people who had low to extremely-low BMI that got pregnant on the pill not once, but multiple times (friend had 3 pill babies and is expecting her first pill grandbaby next spring). Clearly, birth control, even with perfect use, fails people for some reason.
Also the existance of Different "formulas" also muddies the clarity of the issue of birth control medications and their effect on pregnancy. Anecdotally, I have seen many, many "pill babies" who were normal by all appearances and did fine. It would appear, the daily use of the pill early in pregnancy is not necessarily abortifactant nor particularly harmful. But like I said, there are varying strengths and formulas. And people's physiology and chemistry vary greatly too.
So what does this mean for a pregnancy "on the pill?" Well, like I said, there are a LOT of "pill babies" going back to the 1960s that are walking around, perfectly fine. Today's pill formulas are a lot less strong than those of the first generation, designed and marketed first in around 1960, like already mentioned before me. I think the answers are complicated, at least as much so as the complicated chemistry of each individual. Endocrinology is a very complicated and imperfect science, as well.
The resources listed above are good for discussion. But like I said, very unpredictible. The main advice we give any patient, is if she suspects she is pregnant, to stop contraception immediately and get good prenatal care. Many, many people conceived on contraception are all about---and many women I know have had it happen. After all, statistically, the perfect use of contraception can still result in a 1% failure rate. THAT is a WHOLE LOT of people experiencing failure and getting pregnant, anyway.
And one final note, we are sorry to ruffle your feathers, but we get a LOT of medical advice questions here, prefaced with "I am not looking for medical advice but".....and it turns out that way. From a legal standpoint, we at allnurses.com can't be too careful about the exchange of what even appears to be medical advice on a board of nurses. I am sure you understand and thank you.