13 weeks here, had to go to maternal fetal medicine on top of my standard OB for high risk. They actually can put a screen on that shows you which ovary you ovulated out of bc it actually creates a follicle that expels the egg and it remains usually the entire pregnancy. This acts as a block to any other egg trying to “escape”. So under normal circumstances, absolutely not. Anybody can have funky hormones though so the other ovary can possibly do something (mines damaged and can’t produce and they can’t even find it with an US so I can’t tell you what that one looked like).