Can the Microsoft Web Platform Installer install to a remote server? Yes, if you have Remote Desktop access to an administrative account, you can install this on a remote server.
Will it work in a shared hosting environment? No. However, it will work in a Virtual Private Server (VPS) environment or a "cloud" environment like Amazon's EC2. The key is that you need to have a virtual server to yourself, and you need to be an administrator of that server.