Yes exceptions can be made for some vision issues with a SODA or a Special Issuance (probably SI, I doubt you could pass a SODA). But for a first class medical the only cases I've heard of are for one eye (even blind in one eye), or best vision with both eyes slightly off 20/20 (maybe 20/25).

20/40 is pretty bad compared to 20/20, and would IMO not be safe for an airline pilot. I know because that would be me without my glasses...I need my glasses to land a jet at night and spot other planes during the day. So I doubt they would give you a first class.

But no harm in trying.

Also...I'm pretty sure the standard for third class is 20/40, so I think you could be a private pilot regardless.