If you took falling lessons as a kid, and you knew how to properly respond- following the push to a controlled fall, roll, or other redirection- you'd be fine. Sometimes the overreaction is the problem.
Learning to snowboard on dry slopes gave me an instinct to fall with my elbows down and firsts up in front of me, so that I block my body with my arms, but have my fists clenched to protect my fingers. Obviously this does nothing if I don't fall forwards, but anyway.
I disagree. I was by far the smallest kid in my grade, but I took a couple of years of judo when I was 7. It was really useful as I grew up. A big equalizer for me. It does give you an intuitive sense of how to move and a shift your weight in your favor. Even if you fall, you end up falling on top of the other kid. As an adult and for personal defense I think Judo comes right after BJJ and wrestling.
Judo definitely helps. Any full contact martial art will, and Judo is the one with the most contact (at kids level) and lowest chance of serious injury. Wrestling too, but Judo typically covers more.
Lots of close contact will mean you're far less likely to panic in a fight situation. Most people have never been in a fight let alone hit.
Plus the fitness of course. Judo helps enormously with core strength.
BJJ borrows a lot from Judo, particularly the grappling.