I don't think building three slingers without the Agoge policy card is very efficient. Also, an early scout is better at getting era score and spot good city locations and barb camps.
If you want an early slinger for the eureka, why not go scout - slinger - worker - settler - switch to Agoge - build one more slinger per city. Then you saved hammers, have a second city, 3 improved tiles and 3 slingers. Selling your first early luxury is also an option to rushbuy a 2nd worker or a trader. Some people even go scout - settler. I still think worker is better because early Agoge is super useful.
I've been trying the worker-settler thing over the weekend, and it is good indeed. But (even on king, the difficult I usually play) sometimes you'll have 2+ barb warriors, maybe a slinger, coming for you before you get the Craftsmanship Inspiration, specially in coastal or heavy woods/jungle starts. So occasionaly you'll need that early extra slinger/warrior.