Hmm... I'm following four tweeters right now and I don't remember having to type in the authentication details, maybe it's because I don't log out of my Twitter acct. and my credentials are stored in a cookie.
Remember, Awasu has the "Services" mini dialog within the "New Channel" dialog box. You should be able to type in a Tweeter's name, if you know it, and follow them with a couple of mouse clicks.