The answers with the meaning are great, but to be moregive specific, answers: "never" and "no": despite. Despite being in the dictionary, scathe is dead. It's not even in old movies or historical legal documents. It's so dead that it's considered a made-up word playing off of scathing or unscathed. Using it as a serious synonym for injure would be confusing.
Because of unscathed, scathe is vaguely associated with injury. In "I scathed my hand", scathed jumps out -- "you did what? What's a scathe? No wait, I just had lunch. Don't tell me". In a fantasy book we might assume a scathed hand is a magical injury to be explained later.
Also because of unscathed, scathed is a joke word. If you said "2 people were scathed in a car crash", you're making light of their injuries. A listener's thought process might be: "scathed isn't a word -- it's a play on either scathing or unscathed. The opposite of completely unhurt could be killed, or it could be very minor injuries. Or maybe they heard the driver was unscathed and are stupid and think scathed is a word. Or they might have mispronounced unscathed?"
The common phrase scathing insult gives another possible guess. "John is going to scathe you" sounds like made-up teen-age dialogue. He's going to humiliate you, but nothing physical. In fact, Merriam Webster's current online example of recent use has "Monday Night Football debates always seem to scathe a few players". It means mock or insult, as a play on scathing comments.