I think he probably would have backed off -- continued flirting, but not really *serious* flirting -- even if he didn't think her missing boyfriend might be Jien. There's another scene, I forget just where in the manga, where he's hitting on some girl at the front desk of an inn, and when he finds out she's married he keeps up with the flirty chatter but it's all couched in teasing tones of how nice girls like her need to watch out for guys like him; it winds up coming across like "you're cute and sweet and way too good for me, and I don't expect I'd have a snowflake's chance, I'm just flirting because it's the only way I know how to pay compliments..."