I think it depends both on the individual and on the severity of the fall. When I was 11 years old I had a nasty bicycle fall that left me with extensive, painful, road rash (no broken bones, though). Then, after a couple of weeks, and as soon as the scabs were off, I was back on my bike. On the other hand, and many years later, I’ve known about cyclists that witnessed another rider’s fall on a downhill stretch and became so scared they could barely deal with anxiety on every technical descent…
I have had some more falls, but from my experience I think they have only affected my self-confidence if/when I’ve let fear creep in. Most of the times, the falls I’ve suffered were either because I was trying to go beyond what I could technically do at the moment or because I allowed myself to be distracted.
By analysing each fall aftwerwards I’ve learned about what I can, or can’t control.
I’m far from being a pro cyclist, but I think many of them deal with falls in a similar way: focus on what you can control and improve on that (bike handling skills, focus and attention), and wish for a bit of good luck.