Nah, in my opinion it'd be hard to ask your high schooler friend if she's in love with a teacher not academically but in practice, when you know they are already cooking together more or less frequently. There's the stigma around, so it would be easy to make the friend get exceedingly defensive immediately. We actually saw the effect in Kotori's reaction when the friend first marched in. Under similar circumstances I probably wouldn't have asked any more directedly.