PHP is stateless. Each request will run usually in its own process/thread and the process/thread will stop after the script is done. Each instance of a class (also singletons) will thus be existing for the duration of that request. This is unlike c#/.net for example, where the entire web application is run like an application that handles multiple requests. So, no, it is not possible this way.
To share/persist data over multiple requests you will need to use something on disk or some external tool. Think of: sessions, databases, memcache, apc, etc.