Sometimes! I make mine with onions, peppers, and carrots. My favorite diner doesn't shred them, just slices them thin. Some places bake them instead of frying them, too. There's a hashbrown for every occasion, they're not just tinier french fries.
Also, okay, I know it's relatively rare to french your fries these days, but it's even more unheard of to french a hashbrown. (I'd totally eat a frenched hashbrown, though.)