It all depends on how you fall, what you hit and when, and what position your body is in at various stages of this.
If you spend any time on a via ferrata, it’s pretty easy to see where the answers to one or more of these will be ‘not great’, and sometimes ‘really bad’.
For instance, hitting a rung on the way down. Or getting an appendage caught behind something.
But unlikely you’ll die.
And honestly, you shouldn’t fall unless you screwed something up pretty bad to begin with, which is your primary protection anyway.
You’re literally climbing a ladder, this isn’t wilderness trad climbing or developing some new route on loose rock.