Interestingly, when snowboarding was first getting popular with my peers in the 90's (the decade, not my friends' ages), the leading injuries were to hands and wrists. People who aren't proficient in falling tend to try to catch themselves on their most vulnerable body parts - hands and wrists have lots of small bones and are very, very fragile things. The muscles of the lats, buttocks, and thighs are much better at handling impacts.... watch a judo guy take a breakfall sometime.
So, yes, knowing how to fall makes a difference.
Also, being comfortable with falling tends to make people more relaxed when it happens. People who are tense immediately prior to and during an impact tend to incur more injuries than people who are relaxed and loose.
Which is one major reason why in car accidents involving drunk drivers and sober drivers, the sober drivers are usually hurt worse.