If you don't have an online connection for PS3 or Xbox 360, you're going to miss out on a lot of the goodness in Rock Band 2. As anyone still playing Rock Band 1 can attest, downloadable content adds quite a bit to the experience. So will the new Battle of the Bands mode.
Forget what you think about Rock Band and online competition. Battle of the Bands is not a direct band-v-band mode. Instead, BotB offers a series of challenges where bands post scores in an attempt to better one another. Harmonix is promising that new challenges will be added daily, with old ones often cycling out quickly. The plan is for there to always be 5-10 challenges at any time. And if you're worried Harmonix won't deliver on its promise, remember that this is the developer that's managed to deliver new downloadable songs each week for nearly a year. Over the past three weeks, Harmonix has been testing its ability to post a new challenge daily, and so far it's been a success.