You can, but it's not allowed. It's unlikely you'll get caught unless someone reports the domain whois info to the registrar. However, the registrar has the ability to revoke the domain if the info isn't accurate. ICANN mandates that accurate contact info be in the registrar's database.
Get a P.O. Box if you don't want to give out your address.
Further, contact DH support and try to convince them to allow anonymous registrations like godaddy. I submitted that as a suggestion, but they never put it up.