Anything is possible. But highly unlikely. If your super concerned about using public restrooms. Don't use them.
Was a choice between using it or crapping my pants...
I suppose if you had an open sore on your body that touched blood laying on the toilet seat that you didn't see before sitting down....possibly could get hep c.
What Can You Catch in Restrooms?
Bathroom Paranoia
http://www.webmd.com/balance/features/what-can-you-catch-in-restrooms
If you squirm at the thought of creepy germs lurking on toilet seats and faucet handles, you probably spend as little time as possible in the restrooms of your office building, not to mention those in restaurants, hotels and (God forbid!) gas stations. And during those nerve-wracking moments when you dare to venture into the confines of the bathroom, you may find yourself pushing open the stall door with your elbows, crouching precariously above the toilet seat rather than letting your skin touch it, and flushing with your shoe.
But while there's plenty of bathroom paranoia to go around, anxiety might be a little overdone. Yes, there can be plenty of bugs lying in wait in public restrooms, including both familiar and unfamiliar suspects like streptococcus, staphylococcus, E. coli and shigella bacteria, hepatitis A virus, the common cold virus, and various sexually transmitted organisms. But if your immune system is healthy, and if you adopt simple hygienic measures like handwashing, you should be able to deliver a knockout punch to most of what you encounter and perhaps put your "germ-phobia" to rest.
"To my knowledge, no one has ever acquired an STD on the toilet seat -- unless they were having sex on the toilet seat!" says Abigail Salyers, PhD, president of the American Society for Microbiology (ASM).
https://www.healthtap.com/topics/can-you-get-hepatitis-from-a-toilet-seat
It's transferred via blood-to-blood contact.