Yes, it will work. It looks to folks around here like a teenager is trying to make hooch, but it will work. We don't like teens making hooch. Anything longer than a few months of time in the bottle and you want to consider glass, but yes, the juice bottle will work. Any container will work with widely varing results, and any airlocked contained will work okay.
Personally, I wouldn't try and ferment in the bottle the juice came in to save money. If you have a glass jug, use it. They are cheap at any LHBS.
That said, I actually do have a batch of Muscadine + Apple Cider brewing in a juice container right now. Why? I ran out of fermenters, found some Muscadines, and needed to do something with them before they went bad, because my freezer is full. Interestingly, I do my sourdough starters in juice containers, and I find that a slightly screwed on lid actually makes a decent airlock, if you squeeze it you will see. I learned that lesson AFTER one night when I forgot to burp a bottle and had a major sourdough explosion.
EDIT: Looks like you have some equipment already based on other stuff. Why not buy an extra jug and airlock (under $10 at my LHBS) for experiments. Saves you the risk factors with rigged equipment. Metal shards are not tasty.