To me, Haibara is Haibara and Heiji is Heiji, there is no #2.
Not to forget that Haibara is SO different from Heiji.
Err... I was talking about the "knowing the secrect identity part" and "being someone Conan can talk to about Shinichi or the BO" (if he wants) eithout endangering that person. Because - at least for that part - Heiji and Haibara a similar.
what she said to Conan was like a general statement: when a girl stares too much at a boy's face, it either means that he has something on his face or that the girl likes the guy.
Of course even that assumption is up do debate.
Saying: "A boy either hates or loves a girl." would lead to the "undeniable truth" that Conan in in love with Ayumi, because he doesn't hate her.
So, back to Yukikos statement: is it really unusual for someone to look at the face of another person for ten times a day? And does it automatically mean that girl is in love with him if she does?
To be honest, I had never heard that saying before, so I assume Yukiko made it up herself. Why she made that up - think what you want. But I think it was to tease Conan.
Back to the topic, I think the joke (if it's a joke as you say) would work even with Ayumi.
But less funny. As much as I would have loved to see Ayumis confused face upon this question.
She even reminded Conan to take care/protect Haibara before leaving; I don't think that was a joke.
Me neither. But she knew that Haibara and Conan are really in danger should they be discovered by the BO. And she should konw her son well enough to know that he would protect anyone, she was just ensuring him that she supports his descions.