Initially, I was going to post "I don't like skiing, let alone snowboarding" but I realised that the "-ing" words serve as nouns. The same was true for every example I thought of. I can only conclude that we don't use "let alone + gerund"!
If that's not the case, I'm sure another teacher will be quick to correct me.
EDIT: I think I've thought of one!!!
He wasn't smiling, let alone laughing.
I've now seen 5jj's post too and realised that my initial answer to this question was nonsense. However, I've chosen to leave it here as proof that we are not correct sometimes, let alone all the time.