could i do this?

I've often filled my bamboo up to 6 inches or so with no ill effect. Can't speak to what the fish will do to it other than provide more than ample fertilization. I was thinking along the same lines myself, but I was planning on lining the inside of my canopy with them so they would grow out of the top.

A betta should never be kept in a vase. They cannot live off the leaves and roots of the bamboo. Bettas need at the very least a 2.5 gallon tank. Since they are tropical fish they need a heater and every fish needs a filter. Just because they have the ability to breath air doesn't mean they should. They have gills just like other fish and this is how they normally breathe. They also need to be regularly fed, just like any other fish.

The bamboo can defiantly be put in the tank. I have seen many people put them so they are growing out the top of the tank in the back and I have seen people that put them in the filter. Its not a bad idea as they can help filter some of the impurities out of the water.