According to the instructions here [support.google.com] it should be possible, but I'm unable to find "User management" in my account, for some reason. It seems I have no way of adding additional users to my AdSense account. (I sign in using the account attached to my Gmail address.)

Note that you'll still need a Google account for the external e-mail address to use it with AdSense. Unless you add it as an "Alternate email" to your existing Google account, in which you can log in using the alternate e-mail address and your original password (it's like an alias).