By definition, a regulator is not a dead head device as that would be a bubble tight valve. The regulator must be flowing some amount in order to be set correctly (see below).
By definition, a droop curve for a regulator is a plot of pressure vs flow. The weep system that you described is for A) controlling the creep of the regulator and B) has the regulator already regulating so it has a much more rapid response in applications such as N2O or other.
If I knew how to attach a plot of a series of various regulator droop curves I would do so, but I am at a loss on how to accomplish doing that with a big file.

Sufficient to say that some have drastically different curves.
Also to a previous post: Holley carbs with
two needles and seats of 0.110" diameter have a working bowl volume of 0.066gal and a QJ has a working bowl volume of 0.022gal. The N&S of the QJ would have to be about 0.155" diameter to flow the same as the Holley as listed above......Not practical. 0.150" is common, but larger is pretty iffy.
Regards to All that like this kind of stuff,
HB2

Dissident