I'm using Google Apps for my personal domain and email.
Is it possible to use such an account (e.g. "firstname.lastname@example.org") to activate an android device?
Few years ago, Google Apps services were separate from normal Google services. Even cookies were different & compatible to each other. From last year, all Google Apps accounts are normal Google account (You'll have to sign out from normal Google account if you want to sign in with Google Apps account in a web browser).
And, it supports Android too. I've tested it.
Since last year Google Apps accounts are full class citizens. Starting with Eclair android supports more than one Google accounts and since the Market 3.0 update of market all android apps treat all Google accounts on your phone the same way.
Take note however that it is not possible to transfer your Google wallet history and purchases. So if a year from now you want to change your domain name for your email address you will need to keep the old account on your phone or rebuy all your apps again. It is for this reason that I recommend you to create a Gmail account an purchase apps with that not with your apps account.