Interesting! I'd previously only seen recipes for ginger syrup that you added to carbonated water. I'm wondering if the yeast carbonation works the same way as regular carbonation (I've read that carbonated beverages leech calcium from your body).
I don't know about other flavors. It might be worth trying in a small batch. You're cooking the juice anyway, so you should be killing any bacteria that might make it go bad. Whether it will ferment, though, is another question.
Any idea what the lemon juice is in the recipe for? Keeping it from going brown? Tartness? Something else?