As far as I know you should be able to do it just fine as long as the IP is static, because (as far as I know) when you register the domain name you supply an IP. Then anything that searches that domain name will be given that IP address, which it will then follow to your DNS server. So yes, even though its DHCP, you should be able to host just fine, so long as the IP is static.
PS: If its static then it's not like normal DHCP because it will always be given the same IP address anyway, so its more of a reserved address. It wouldn't work like most DHCP because it doesn't get given a new IP each time it starts up, so this is none or your concern.
~ Paul