Assuming you chose a strong passphrase, which you safeguard properly, and barring keyloggers, you should have absolutely no issue having your encrypted database published on the front page of google.com and offered to everybody.
Just ensure you have a few million key transformation iterations to really harden it against bruteforcing attempts.
In reality, though, given that you can never be 100% sure you don't have a keylogger or other malware, you shouldn't really volunteer half the keys to the kingdom (= the database) to the world.
Actually, if you handle third party data this could even be a breach of regulations (think HIPAA)