There are no strong reasons why it should not work on Windows Server. You should be fine developing such a service.
Artem Taturevych, Application Engineer at Intercad (Australia)
translationXpert – add-in to translate SolidWorks models
myIntercad – an integrated tool for SolidWorks Professionals
I don't think SolidWorks will install on a server machine. But from your description, I don't think you need SolidWorks itself. SWDocumentMgr should be enough to get BOM information.