Based on personal experience, no. I have not had to trim any pubes recently and do notice none have yet reached the bottom of my trouser legs.
I don't think there is a predetermined length; hair is dead and there is no means of communicating to the follicles that it has reached some acceptable length, although there could be a time based control so that it simply stops after a certain time or falls out.
I suppose that hair could be limited because larger hairs are susceptible to being pulled out but I guess this does not apply to eyelashes though they seldom get longer that a few millimeters.
Looking at other mammals such as a horse, the mane grows much longer and (I think faster) than body hair. I see no reason why humans would have different mechanisms.