No, they cannot retrieve the passwords. In a secure password system, such as those used by Google, Yahoo, Banking sites and nearly all other major websites... it is not possible to recover passwords.
I don't just mean that there is no option for administrators to access your password, I mean that your password is never stored in a database and it is simply not possible to retrieve it.
This is because they use password hashes. When you created your password during sign-up, the server took that password, performed a complex mathematical algorithm on the password text and converted it into a hash, a string of characters that uniquely represents your password.
Your original password cannot be recovered from the hash except through brute force, i.e. trying billions and billions of possible password combinations to find the one that produces the same hash, which would take an impossibly long time unless your password is very simple.
When you login, the server again takes the password you just entered and converts it to a hash using the same algorithm as before. The hash of the password you just entered is then compared to the hash generated for your original password. If the hash is the same, it means you entered the same password and you can login successfully. Your actual password is never stored during this process and remains a secret to everyone but you.
In summary, your Google Mail account manager could not possibly retrieve your password, nor could an employee of Google.