Yes, you will!
Each monthly Update has a set number of Adventures - depending on how many games/toys are released that month. I think most months have about 6 Adventures to it.
Once you finish all of August's Adventures, you will go back to where you left off last, until you complete all of them. Then you'll go on to another month, etc, etc, until you are finished with all past Adventures. Once that happens, you will find that Bloo says something like "We've done a lot of adventures lately, let's take a break" or something like that. So you won't be able to do any more. So basically, you sit and wait until the next Update happens on the site.
If you are only a couple Updates behind, you can usually catch up within 2-3 months. I was all caught up, but missed out on all of June, because of the Shockwave glitch. It's taken me all of July and Aug to catch up. I should be finished by the Sept Update, though. If you have more than that to catch up on, it will take you longer, so you'll have plenty to do all the time. The fastest way to get all caught up is to play the game every day. Before long you'll be all caught up!
~Vicks