The only times in canon we've ever seen Harry cry have been when people have died and so I think it would be unlikely for him to become teary-eyed, because he tends to bottle up his emotion a little more than that, generally. I think it would be very likely for him to share an intimate smile with Ginny and maybe squeeze her hand or something and inside he might be struggling with a lot more emotion, but I'm not sure that it would really show to the extent of welling-up. Also, I would imagine Harry would be far more pleased and excited than overly emotional about it anyway.
Just my take on it. Hope it helps.