I can't answer for your situation and I've never tried it but...... In my own case, I am SO reluctant to admit to having a problem of any sort, if I ever did I'm pretty sure my T would take it VERY seriously. I don't think it really IS a rhetorical question. I think it's a chance to ask for help if you feel so inclined.
What I would EXPECT my T to do, and any one else's too, is stop and deal with the situation, how ever long it took. Even if he/she was late getting home or late for their next appointment.
I have situations come up all the time where events with one client make me late for the next one. If someone has a problem with that, too bad! My goal is to dedicate 100% time and attention with the first client, finish what needs doing, and THEN move on. What goes around comes around. If I'm late to your house today, I may be late BECAUSE of your situation the next time.