I dont see any reason why it wouldn't work. but i do believe that the reason fermented veggies are so affective is that the microbes bury themselves deep into veggie fiber and that way they survive the stomach acid and have a sort of platform to start a colony in the intestines. thats my theory anyway.
all i can say is try it, it may very well work out.
have you ever made kvaas? its great. its basically a couple slices of beets in a glass of water with a fermenting agent. very powerful. i like to add a bit of the LB17 fermented cabbage to it, works great.