Plus if you go through the house and go south from Cerulean, then take the underground path to pass Saffron (can't get into Saffron, the guards are still thirsty...), you can get to Vermillion without beating Misty. You can't fight Surge, of course, without Cut, but there are some stronger trainers and, in the Pokemon Center there's the chick that gives you the little beepy thingie that makes trainers you've already beaten challenge you again, which is great for leveling up if you don't want to lose all your cash to Misty. ^_^()
*got through her with only her Charmeleon and Meowth, 'cause that's the way I roll*