Nah, the manga is only half-ways, no way they start going out yet. I suspect they have a few mishaps like you said during the date, both being nervous and all that, but afterwards being more themselves they get into the groove and are about to confess to each other, ...and suddenly an old acquaintance(of course a girl) of the mc happens upon them and the chapter reads 'to be continued'...Everything is going to go wrong, then Hiiragi gets depressed, then Kotori cheers her up and then Hiiragi says she was supposed to confess and he confesses then they go out
for 1 chapter, then the manga endsthen they go out