I have to disagree. Coming from Kosuke, this was probably about as serious as it could've been, honestly. (and props to him for just coming right out and saying it, too—no embarrassment, and little to none of the usual comically exaggerated theatrics)
I think Ibarada's reaction is meant to convey something along the lines of conflicted anguish. Like she'd been secretly hoping for this the entire time (obviously), but also dreading it in some way because of her own circumstances (i.e what we know so far about her family situation and such) making things a lot more complicated than they seem.
She's probably going to reluctantly turn him down, thinking it's for the best, thus leading to an entire arc about her issues and helping her overcome them so she can reciprocate Kosuke's feelings in earnest and with a clear conscience.