TLDR: The mechanic is almost certainly right in this case. Wear it into the ground, or be prepared to replace the chainrings, freewheel, and chain together at this point. That's an insanely long period of time to go without a chain replacement assuming the bike has been ridden at all regularly.

He's probably making a fair suggestion regarding a new bike, particularly given the amount of labor required at a common shop rate. Still, many of those older Treks are fine bicycles, and while I might explore the idea of a new bike with a customer, I would definitely also lay out clearly a plan for repair. I'd repair it if it were mine--I like most Treks of that approximate vintage.