I'm going to say

no

because you said:

hate any dry patch of grass down to the last little spot on a single blade; there is also no horizontal movement of water once it hits the ground

and coupled with

what I consider a sprinkler, being a device larger than a blade of grass fed by a hose larger than a blade of grass, means that somewhere in your sprinkler setup is at least one blade of grass that is in the rain shadow of either a sprinkler or a hose, and given that your water doesn't run sideways, that blade won't be watered.

Of course, you could take the unconventional approach of

using your considerable engineering prowess to suspend your entire sprinkler network upside down over the lawn, in which case see other answers, or read on if you want to save money..

Which would mean, if you have an appetite for such wizardry, I can comfortably assert

yes you can water the entire lawn, with one sprinkler: mount the sprinkler on a cart attached by a Nmm wide hose at least 4500mm* long, to a central cylinder of radius 159-N/2 mm. Ensure the cart has a system to drive the wheels based on the flow of the water. Turning the water on will see the cart drive round the central cylinder in a spiral that becomes 1m closer to the center each circuit. At the point the cart reaches the center the wheels are halted and the flow stops, saving precious water, and given that the central pole radius is less than the sprinkle radius the center of the lawn is already well watered in advance of the cart reaching the stop point

*it can be marginally smaller but all values are approximate given the spirit of the answer

I'm going to say

no

because you said:

hate any dry patch of grass down to the last little spot on a single blade; there is also no horizontal movement of water once it hits the ground

and coupled with

what I consider a sprinkler, being a device larger than a blade of grass fed by a hose larger than a blade of grass, means that somewhere in your sprinkler setup is at least one blade of grass that is in the rain shadow of either a sprinkler or a hose, and given that your water doesn't run sideways, that blade won't be watered.

Of course, you could take the unconventional approach of

using your considerable engineering prowess to suspend your entire sprinkler network upside down over the lawn, in which case see other answers, or read on if you want to save money..

Which would mean, if you have an appetite for such wizardry, I can comfortably assert

yes you can water the entire lawn, with one sprinkler: mount the sprinkler on a cart attached by a Nmm wide hose at least 4500mm* long, to a central cylinder of radius 159-N/2 mm. Ensure the cart has a system to drive the wheels based on the flow of the water. Turning the water on will see the cart drive round the central cylinder in a spiral that becomes 1m closer to the center each circuit. At the point the cart reaches the center the wheels are halted and the flow stops, saving precious water, and given that the central pole radius is less than the sprinkle radius the center of the lawn is already well watered in advance of the cart reaching the stop point.

Bonus: considerably less powerful I dare say - the limit rather depends on relatively intangible physical properties of the entire affair, if you're prepared to engineer a spiral with a LOT of turns and wait a long time for your tiny cart to execute them, a puny stream of water carried over a hairlike hose

*it can be marginally smaller but all values are approximate given the spirit of the answer