If there is any doubt there is no doubt. The crew concerned showed an apauling lack of judgement and were luck to get away with it. The FO showed a total lack of knowledge by trying to tell you how deicing would make the problem worse, had he not heard of hold over times and 2 step procedures?
The B737-800 does suffer badly from NEI and Boeing have approved an area on top of the wings to have iceing present, it is marked with black lines. Not all aviation authorities have approved this measure, I also personaly believe it could lead to abiguity in what should be a cut and dry stiuation.
Ice the thickness of fine sandpaper reduces lift by 30% and increases drag by 40%.