The only case I would recommend The Brain go with a single online file storage provider (like Dropbox) is to contract out the storage for their in-house WebBrain or syncing service. In that case, cut out the middle-man (DropBox) and go straight to the storage provider (like Amazon S3) for much better pricing, great API, etc.
As for Users syncing their Brain in their personal DropBox (or any online storage service) account, that's easy. Just set up your file syncing client to include your Brain folder. You can have your Brain synced to Android, Blackberry, iOS, PC, Mac, and Linux right now using existing technology. The problem is having the files synced to your Android, Blackberry, or iOS doesn't let you view/manipulate them and that's not something DropBox (or any other hosting provider) can help with.
Getting the data to sync between computers running The Brain isn't the problem though. The problem is that people want to view and manipulate their brains from their assorted mobile devices. If you are suggesting that The Brain work with DropBox so that users pay DropBox for storing their WebBrain, thus removing the 5GB storage limit, I would caution against choosing a third party provider for the customer.
1. While convenient for existing Dropbox customers, it is very inconvenient for people who are customers of SugarSync, OpenDrive, Rackspace, Amazon S3, JungleDisk, Box.net, ElephantDrive, FlipDrive, iStorage, ADrive, etc., etc., etc.
2. In terms of cost, Dropbox is one of the most expensive options for storing a WebBrain. Granted, they have a lot of other features, but none of them are necessary for hosting a WebBrain and you're wasting your storage dollar. I can get 1 TB for around what DropBox charges for 100GB.
I will agree that, if WebBrain happened to use the online storage solution that I already use, I'd be delighted. However, regardless of how valid any of my three points are above, the truth remains that there are way too many players in the online storage game to assume even a majority of your users would be happy with picking one of them like that. People place different weight in features, security, price, reliability, redundancy, transfer speed, etc. and what's perfect for one person could be perfectly crap for another.
Of course this is all assuming that the 5GB cap is strictly financial and not a cap that is in place because of technical limitations such as 'going bigger than that on a WebBrain uses too much memory and causes the viewer to crash.'
If it is a financial cap, I'd rather WebBrain stay hosted here and they just change the billing structure to something like 5GB included and $xx for overage or $x per GB storage and $y per GB transfer. There are storage providers they can contract with that have well developed API's to handle automating the billing based on storage volume, transfer volume, etc. Amazon S3 is one great option.
If the 5 GB restriction is in place due to technical limitations and not financial, that's a whole different problem.
All of that said, I always prefer a client over a web app any day of the week so you have my vote for an Android app. I'd pay a lot for that.