Nope, I'm afraid they wouldn't fit the bill for several reasons.
Teenagers don't drive, so couldn't get my cat to the vet in an emergency.
They would also be highly unlikely to know the "warning signs" for lots of illness in cats, and therefore wouldn't realise when a vet was needed in the first place.
I've seen cats go from perfectly healthy to critical in less than 24 hours. I wouldn't trust a teen to know the signs of say, a urinary blockage or stress cystitis - I mean, why would they? But both conditions require pretty urgent treatment or they can quickly turn fatal, which is why I would only ever pay a professional to care for my animals.
I've had a few animals get sick or injured in my care. Nothing serious, but they still required vet treatment and I had to drive them, wait with them at the vet, contact the owners, make sure the animal was cared for and medicated properly etc.
Not something I'd trust a local teenager to organise and sort out, I'm afraid.