Reading the OP. Is he saying the FD bank angle selector is required by his company SOP to be set at 15 degrees on all take off's (in case an engine failure occurs in the climb to 1500 ft) and not changed until above 1500 ft? The 737 has a bank angle selector for the flight director. Most operators I know of have it set at 25-30 degrees for normal flight. If the departure requires a curve after engine failure at V1 then it is a simple movement to switch the angle of bank limitation on the FD selector to 15 degrees. As the gradient of climb varies only a slight amount between V2 and V2 +20, then even if an engine failure occurs seconds after lifting off, the aircraft will have already accelerated during the rotation sequence to V2 + 15-25 and a 30 degree angle of bank is quite legal and safe.
It is unnecessary and proves nothing, to limit the angle of bank to 15 degrees on all engines until reaching 1500 feet - just in case an engine should fail before 1500 ft.
However I may have misunderstood the full meaning of the original post