No matter how unfastidious and unobservant he was when he married Elizabeth, he'd probably eventually figure out what she was really like, after it was too late! I think that was part of Line's point.

It's possible, I suppose, for him to be shallow enough not to ever really care, to never wake up, but that seems unlikely given that we've been told that he was unhappy in his first marraige. If he is capable of being disenchanted once, it could happen again.