From the standpoint of performance requirements, it is pretty clear that the minimum climb gradients have to be complied with. If the second segmnent is, for whatever reason, extended above 400 ft GND, than the requirements for second segment still apply - until acceleration altitude, when third segment starts and other rules apply. So if anti-ice is needed during that period, this will affect the take-off performance calculation. Otherwise, if an engine would fail at, say, 600 ft which anti-ice now ON, the climb gradient could in theory be less than 2,4% gross and therefore less than 1.6% net, which is not a good idea (and of course that would be illegal for any FAR/JAR 25 aircraft).
On the other hand I assume that the performance of the 737 NG is so good that in most cases the aircraft will not be at the minimum 2.4% gross climb limit with temperatures in a such a low range that anti-ice is required. But I could be wrong on this one.