How do I access a function provided by a service resource module?
Functions are exposed via service resources, by a module implementing hook_services_resources().

You should take a look at whatever module your using to provide Services functionality for the private message module, specifically its implementation of hook_services_resources().

If you see an entry with a callback of _privatemsg_services_unread_count, then the function you want is available via a resource. If not, it currently isn't, and you can implement hook_services_resources() yourself to expose it.