You can animate hair growing by keying the scale on the hair follicle shape(for dynamic hair), although there is no clip attribute. (the pfxHair node is the closest to the pfx stroke node, but does not have the clipping attributes)
However you can do something a bit like the stroke min/max clip by using the hair width scale ramp. If converting to poly then there are no polys where this ramp is zero. The indice positions can also be keyframed if desired.
Duncan