hmmm, i gotta wonder how that would help. beta carotene? lol. I know that comes from plants, but I don't know if it acts as a fertilizer on plants. If I tried it, I would not use a "product" in a can from the store. (if there is even such a thing as carrot juice in the can) Seems you would have to make it from real carrots with a juicer.
If you try it, let us know. Maybe the vitamins in carrot juice acts like a fertilizer enhancer, haha.