I'm a user of portableapps.com apps and have Firefox and Chrome in Dropbox. They work great.
But, if I copy the same setup into an encrypted folder and run the browsers, they are unable to load anything on the web. It seems that any program that tries to do any networking fails. The reason I say this is that I also have Calibre portable in Dropbox and the same copy also in my Boxcryptor folder (testing out Boxcryptor with this problem) and it will not download any metadata or send emails.
The errors from all the programs relate to DNS errors, but they work just fine if not in the Boxcryptor folder.