HELL NO! Well unless you encrypted it with a strong password. But Dropbox (i.e. their employees) can access your data. And depending on where they host their data, so can the particular 3rd party hosting / cloud storage company (maybe Amazon or whatever).

Not saying these companies are untrustworthy, but you simply don't want to take this risk. Especially because IF your coins disappear, there's no way to proof it was them.

Wuala.com (an alternative to Dropbox) is safer because encryption occurs client side there.

Then again, you shouldn't have an unencrypted wallet on your PC anyway. Suppose someone breaks in and takes your PC. Or you lose your laptop or whatever. Simply do NOT mess around with your money.