On selection of TOGA the nose is going to come up at you FAST, you're going to climb like a homesick angle. Even if the go around was initiated during the flare it would take no time at all to get to 2500'. You'd be there before you know it.
No, the NG flies quite nicely if you go around. It produces thrust to give a climb rate of 1000-2000 ft/m unless you press TOGA a second time. It climbed 2500 ft, not to 2500 ft if I understand it correctly.
The NG flies well with ice on it. It flies well with a lot of ice on it. They would have been pretty much ice free when they went around, and I don't see how they could have accumulated enough ice to fall out of the sky in a 2500 ft climb.