Um, what do you want to do with it? If you plan on lighting it from the inside (like a giant light cover) then painting it white will allow little to no light transmission. Well, I guess you would have to factor in the type of paint you use and how bright the light is. Depending on the paint you use, it might not stick to the bottle. The bottle also flexes a bit so that can cause paint cracking and peeling. I use 2L bottles to make water rockets with my kids and normal spray paint comes off. Especially after you pressurize and launch it a few times.
You might want to try sanding it a bit first to see how you like it. If you use a fine grit, you will end up with a frosted look. If nothing else, it will help the paint to stick. You also might want to try the Fusion line of Krylon spray paint. It is supposed to bond to plastic better than normal paint.
If you paint the inside, then you don't have to worry about it scratching off. Since spraying won't work, use a solvent based paint, not latex (it won't stick). It will take a while to cure though.