As long as you know how to sharpen freehand then yes, you could do this. You would wantvto use te corners of the stone to sharpen the recurve. With that said, you are going to want stones in different grits. By the time you buy one of each stone you might as well have just bought the sharpmaker. For a cheaper alternative look at some of the other rod based sharpening systems. Check out the lansky croc sticks. They are a similar sharpening system to the sharpmaker but slightly less refined. I believe Smith makes what they call their "3 in 1" sharpening system which includes rods in a V shape like the sharpmaker but also features a diamond bench stone.
Truthfully though, I would just save up and get the sharpmaker, its definitely worth the $50 it costs.