To me the entire point of a password manager is to solve password reuse. I can only remember a small number of high-quality passwords. I use one of those to secure my password manager, and I consider that password good enough to be unbreakable even if stored with a simple unsalted hash (and I know KeePass does much better).

I would be comfortable hosting my password file publicly. Any benefits from Dropbox authentication are just defense in depth (and privacy benefits).