I certainly would not see a problem. Your fermentation is going to kill off any potential bacteria the would spoil the juice. As long as you follow standard protocols of pH levels, shoot for an appropriate ABV (10% or more typically) and keep the batch in a bucket covered with a cloth while fermenting everything should be fine.
Check the wording on the package too. They vary wildly like:
- Best By
- Use Before
- Expires on
- Best Flavor if used by
- Discard after
- Sell by
- Use before or freeze before (Very common with meats)
This is one area of food labeling that is a real zoo and you have to work to understand it but keep in mind, they'd rather you throw that food out and buy more than risk you have a bad experience. They also have to add buffers in those dates for legal protection.