I'm not sure about being picked up on scans, but I think (think being the operative word here) that the placement and look of birthmarks is somewhat hereditary, so, that might offer you some comfort.
Also, anecdotally, my DD had a bright red mark on her eyelid when she was born, she's 7 now and it's not visible at all. I can't remember what age she was when it faded but for the first month we all thought it was a birth injury (forceps) until it stayed out for a few years.
Also anecdotally, I went to school with a girl that had a huge strawberry mark on her chest, just above what turned into her cleavage. When we were 13-ish, she got it removed on the NHS, very minimal scarring back then, we're heading towards 40 now so they'd probably be able to remove a more pronounced birthmark without any scarring now a days.
Don't worry yourself OP, there is literally nothing you can do to mitigate against it, as long as baby is healthy anything else that comes along you can and will deal with!
Good luck for your birth and try to relax and enjoy your last couple of weeks before baby arrives! You've plenty of time over the next few years to stress the small stuff!