Well, not exactly, only the area to the fileserver that people need to write to. So segment off a directory where the IUSR has r/w access, and the rest of the server IUSR doesn't.
You can't have the system impersonate the user who is currently on the system because you'd have to shut down IIS, change the user IIS uses, then start the server again, all dynamically. You're going to have to do it programmically and trust your security model and users.