We did that with big tomato juice bottles and milk jugs one year. DH and I lived in our motorhome for 9 months while we saved up to buy a house. We'd only cut a whole barely big enough for the young plant to fit through at the bottom and hung them upside down on the rv mirrors.Actually I thought he drew it pretty good. They sell setups like that, but I am not paying ten $ for one. I don't like the thought of the plant directly in the bottom either but I guess it doesn't matter even with them planted in each side water still runs all over the plant.
White tomatoes! They don't sound yummy. Doubt they have much lycopene. I'd try them though.
I also wrapped the jugs in duct tape (that's all we had), due to the small hole at the "top" it kept moisture and heat really well on the roots. While the plants failed to grow a lot (bought them at the local hardware store and I suspect they are not for our climate) we did get 2-3 tomatoes from each plant.