You can and it works. I have about 40 branch offices and - for political reasons - a management decision was made to give each a full server infrastructure. For financial reasons it was a single-server environment in each, so it's all DC/File/Exchange (this was in the Windows 2000 days).
However, management of it is a nightmare, and my preferred rule is "a DC is a DC and nothing else goes on it". These are your most important servers, and if your AD goes funny you will have a horrible time getting it back right. If you can, give yourself the best chance of avoiding this by having dedicated DC roles. If you can't, beg, scream, whimper, bribe, threaten, prophesy, or whatever it takes to put yourself in a position where you can.
This has been a fun topic of discussion on Server Fault. There appear to be varying "religious views" on the topic.
I agree with Microsoft's recommendation: Use a sub-domain of the company's already-registered Internet domain name.
So, if you own foo.com, use ad.foo.com or some such.
The most vile thing, as I see it, is using the registered Internet domain name, verbatim, for the Active Directory domain name. This causes you to be forced to manually copy records from the Internet DNS (like www) into the Active Directory DNS zone to allow "external" names to resolve. I've seen utterly silly things like IIS installed on every DC in an organization running a web site that does a redirect such that someone entering foo.com into their browser would be redirected to www.foo.com by these IIS installations. Utter silliness!
Using the Internet domain name gains you no advantages, but creates "make work" every time you change the IP addresses that external host names refer to. (Try using geographically load-balanced DNS for the external hosts and integrating that with such a "split DNS" situation, too! Gee-- that would be fun...)
Using such a subdomain has no effect on things like Exchange email delivery or User Principal Name (UPN) suffixes, BTW. (I often see those both cited as excuses for using the Internet domain name as the AD domain name.)
I also see the excuse "lots of big companies do it". Large companies can make boneheaded decisions as easily (if not moreso) than small companies. I don't buy that just because a large company makes a bad decision that somehow causes it to be a good decision.
Best Answer
According to this link and the Windows Server 2008 R2 Best Practices Analyzer, the loopback address should be in the list, but never as the primary DNS server. In certain situations like a topology change, this could break replication and cause a server to be "on an island" as far as replication is concerned.
Say that you have two servers: DC01 (10.1.1.1) and DC02 (10.1.1.2) that are both domain controllers in the same domain and both hold copies of the ADI zones for that domain. They should be configured as follows: