It is possible to have hundreds of different websites all pointing to one database. You just need to make sure your host will allow your different domains/sites to connect to the same database. After all it's not the domain name that allows communication between the web and data tiers, it's the hosts server configuration and policies.
For example I host one website, but have been thru 2 or 3 different domain names over the past few years. All of the domains point to the same website inside of IIS. Or in the case of one sub-domain points to a different website inside IIS, but still talks to the same database. It's al in your connection strings.
However you will most likely not be able to have the database server on one host, and sites on a different host. These ports are normally shut down for standard communuication.
Your best bet would be to talk to their technical support to see if it's allowed.