In total, druids remain in a beast wildshape form for a number of hours per day equal to their class level.  That's potentially a lot of time, for archdruids it could be all their time, and, this being the case, I was wondering whether this might have been one of the motivating factors for druids developing their own language.

Could druidic, to any extent, be usable between druids in some/all beast wildshapes? If so, how could it work?

I figured Druidic had it's origins as an advanced system of trail markings more than a spoken language.

Thus you can quickly scratch it out on the ground.

I've always imagined it to be a secret society language for select membership such for a hippy, occasionally reclusive Illuminati. 

In use with signs, a regular purpose might be to indicate things like "this plant may eat you" or "smoking this herb's great".