NOT true! The trailer is added weight the ABS only activates to keep the wheels from locking on the bike - It makes no difference what the trailer is doing it (the bike) doesn't know it's there. The trailer only adds to the total stopping distance due to the extra weight.
ABS only works with full presser on both brakes equal - just like in a car (you don't pump the brakes anymore or you shouldn't) if ther car or truck is equipped with ABS even if it's pulling a trailer, Now if the trailer has electric brakes that a whole nother subject.
The ABS should activate when the wheel sensors report a wheel to be locking up. Total load weight on the bike or behind the bike being irrelevant to that activation. ABS watches for wheel lockup.
If more total load requires more overall breaking that suggests to me wheel lockup potential at potentially lower speeds acting within the same distance. If a breaking scenario might lead to this circumstance than ABS managed breaking without lockup is going to be beneficial to overall control. No matter whether lockup might occur at lower, similar or higher speeds, however, ABS managed avoidance of lockup is going to be beneficial.
Wheel lockup without the trailer can be problematic enough. Any time it might be avoided with the trailer has got to be a benefit.