It is my understanding that there are two types of brakes you'll find on trailers, the ones activated by a weight that swings forward under the force of the truck's braking, and electric ones. Neither are anti-lock or anything fance, and neither are really designed to provide actual stopping power, the drag they add is meant to help maintain control. Most of the braking force is done by the truck's front wheels.

I don't think it's impossible for there to be a spot on the performance envelope where you'll stop a few feet shorter with a lightly loaded trailer, but I bet it's not particularly large.

It is impossible with a trailer with no brakes.