Yes, you can do this.  The only complication is that you'll need to store the password by returning a tag from the authenticator's authenticate function, as shown below:
function checkUserName(userName, userInfo) {
    return userName=="test";
}
function authenticate(userName, password, authInfo) {
    return {
        isCorrectPassword: password=="test",
        tags: {
            password: password
        }
    };
}
Note that I've hardcoded it to accept only the credentials test/test.
Once you've done that you can access the user-name and password from any JSS process trigger as follows:
var userName = system.user.userName;
var password = system.user.tags.get("password");Does that answer your question?