I've never waited for Green Day before, but I've waited for actors and other musicians at the stage door plenty of times. It's perfectly possible to see them, since they have to get into and out of the venue somehow. Unless they have a private coach/car area where they can go straight from the door to the vehicle with no public access. I don't know the specific venue, but most aren't like that. There are 3 key things to remember:
Be patient - bands like to take their time coming out at the end. They also like to arrive early. If you want to catch them, you're gonna have to wait for a while, be it before or after the show.
Be respectful - whether it's Billie Joe or some random roadie, it's really important. This is their work day, and any time you're there will be a busy time. They're much more likely to take some time out and engage with you if you treat them respectfully as humans rather than yell at them. That random crew member might just be the guy who tells the band that there's a really nice fan waiting outside to speak to them. If the band are tired and on their way home, they're much more likely to stop and engage with you if they can see that a conversation will be easy.
Don't get in the way - often venues only have one main stage door, and there'll be gear and not-the-band people rushing around. Getting in people's way will piss them off and is a surefire way to get thrown out before you have a chance to meet the band.
There seem to be plenty of people on here who've met the band and can probably offer far more specific and useful advice, so I'm sure, if you do go, that you'll be going prepared!