Ask yourself is this would be an appropriate job for a toddler. That's about the mentality we're talking about here. If he's not safe to drive, I'm surprised his doctor hasn't pulled his license yet.
Narcolepsy dogs that I know of have been trained to respond when the handler is down, not just drifting off. Think about how hard it would be to define "drifting off" in terms a dog could grasp. You can send her this handbook, which might make her rethink her ability to owner-train:
http://www.deltasociety.org/Page.aspx?pid=303#MinStdsShe mentioned a grill, which I take to mean he works in food service. A service dog is not going to be permitted in food preparation areas. In dining areas, yes, but not in food prep areas. So that's not going to work for the grill issue, plus there's the issue of what to do with the dog while he's at work.
It appears to me they can spend 18-24 months training a dog, with her driving him in the interim and knowing he can't use the dog at this particular job, OR for less than the cost of one bag of quality dog food he can get this instead:
http://www.sav-a-life.com/Doze_intro.htmAlso remember that a diagnosis of narcolepsy does not automatically qualify him as disabled. That's a question for his doctor, but honestly if he was disabled I'm pretty sure the doctor wouldn't be letting him drive.