It would work, however it takes a lot of water to dissolve borax and most hose end sprayers are 8-16oz. You can probably only dissolve about 3-4 tablespoons in 16 ounce of water. You would also have to wash it off the grass immediately.

I have found wet sand to be a great carrier for borax. It mixes together very well since the particle size is similar, and then you can just walk around, grab a handful of the mixture and sprinkle it out of your hand as you walk the area. I did 3,000 sq feet in about 10 minutes and used 12 cups of sand to 12 tablespoons of borax mixed in a bowl. You can use more sand if you want.

I have a 4g backpack sprayer. I've also got 30,000 sqft! Good thing was I needed to get some milo down but boy did it take some time in this heat