Sounds like it might work a charm. I would be careful about particulate sizes, though, so as to not clog the system. Sprayer nozzles can be finicky.
If you had a screen on the outflow, well you'd have to clear the screen if particulates were an issue, but you wouldn't end up having to dig up your sprinkler system.
My only other question would be what the effect of being sprayed into tiny droplets in the air would be on the bacteria and fungi living in the extract. Would it just give the droplets a
boost of oxygen before hitting the ground, or would they be harmed by the pressures involved?
Dr. Redhawk has the description of a hose-based subsurface inoculator consisting of a flattened pipe that gets thrust into the ground with a valve to a pipe onto which a hose to the extract barrel goes. The pipe gets thrust into the ground, the valve is opened, and the whole device is lifted out of the ground, closing the valve as the tip emerges.
I would suspect that the extract would work mostly as intended, but you'd be diluting it, so it may act more as a foliar spray than a soil inoculation.
But let us know how it goes, and good luck.
-CK
A human being should be able to change a diaper, plan an invasion, butcher a hog, conn a ship, design a building, write a sonnet, balance accounts, build a wall, set a bone, comfort the dying, take orders, give orders, cooperate, act alone, solve equations, analyze a new problem, pitch manure, program a computer, cook a tasty meal, fight efficiently, die gallantly. Specialization is for insects.
-Robert A. Heinlein