It seems like the most secure way to use it, assuming you've enabled back ups in 1Password to iCloud or DropBox.
Whenever I need a password I just grab my phone and look it up, then type it in. Sure, I have to manually type passwords, and my randomized passwords all have a minimum 18 character length, so it takes a bit longer. It's a plus though, because over time I memorize my passwords through repetition. If you have the program on a desktop and it just copies/pastes your password, you'll never memorize it.