Yeah, they do. And from what I've seen, things are going well. The latest chapter shows them going to a hotel or onsen (I think?) after their date, so it's easy to guess what might happen next.
@EG0611
Japan has a National Healthcare System, so when someone who's normally strong and healthy (teenagers-middle aged) gets sick, going to the hospital isn't a big deal.
I agree that the dude was overreacting, but pro-active treatment ensures the best outcomes.