While it is certainly likely that Elizabeth had illegitimate children, I think it was Catherine the Great, who was pregnant with the son of Gregory whatever his last name was, in the early months of Peter III's reign, and it was hard to conceal it, and made it harder to fight for her rights. She gave birth before the overthrow of her husband secretly, while the court was watching a fire that had been delibaretly set as a distraction, since Peter liked to watch fires. I have heard there was a possibility that Elizabeth didn't fight for her right to the throne at one time, earlier on because she might have been pregnant. It's certainly likely.
