The more I think about this, the more it doesn't sound feasible at all. Sure you can generate steam and send it up a tree system. However, that steam will have cooled SIGNIFICANTLY going up the tree and out into the bottles. All you'll be sending into the bottles is distilled water. I don't see a significant difference between a tree or any other type of manifold. Same problem. The steam will have cooled before it hits the bottles.
Even with my handheld steam cleaner, you can hold your hand 6" from the spout with it blasting out. The steam has cooled by that point already to worthless temps.
If anyone has tried this, I'd be curious what temp the steam is coming out the ports into the bottles.