Can "let alone" be used this way?

Solution 1:

let alone OED

e. The imperative let alone, or the present participle used absol., is used colloquially with the sense ‘not to mention’. (The object, whether noun, adjective, or clause, in this use follows alone.)

Your usage is grammatical and acceptable.

As in:

• 1966 Listener 20 Oct. I cannot say that I ever felt anything like twice as old (let alone twice as wise) as my Polish friends.

• 1974 L. Deighton Spy Story He'd never be considered for a high security clearance, let alone a job in the Service.

Solution 2:

The meaning of the second sentence can be completely differently from the first.

1. The man is too severely injured to be saved even by a doctor, let alone by a layman like me.

This means that the man can't be saved by a doctor, and certainly not by you, since you aren't a doctor.

2. Even a doctor can't save a man so severely injured, let alone a layman like me.

Depending on how you interpret it, the syntax could mean that even a doctor can't save a man so severely injured, and a doctor certainly wouldn't be able to save you.

Of course, the interpretation of the second sentence I give doesn't follow any logic from the sentence itself; however, the syntax certainly allows it. It would only make sense if laypeople, by definition, were always more than severely injured.