I'm afraid this is a database we have not tested. Actually the best source to get this information is the vendor themselves. You may want to contact them and verify if their product will run on a Windows 2008/IIS 7 platform configured as a shared hosting environment.
A lightweight document-oriented database like that seems like kind of a step backwards. I understand that it has its uses, but it wouldn't scale up, and I could foresee more than a few potential problems there from a host's standpoint.