The 1Password people certainly support using Dropbox.
In general, 1Password uses good encryption and Dropbox keeps your files pretty private. So if you have a good master password, you shouldn't have to worry.
However, giving anyone else any sort of access to your entire password cache is always going to be less secure than keeping it to yourself. Whether the benefits outweigh the risks depends on how valuable the information the passwords protect is.
If you have nuclear launch codes in 1Password, DON'T put them on Dropbox. Otherwise, GO AHEAD.