Force Stopping an app doesn't mean that it was running before you force stopped it. It's just a way to let the user tell Android they don't want the app to be started again, until the user launches it again manually.
If you force stop an application, it won't be able to receive GCM messages until the user manually launches it again, because the GCM background service won't be able to launch it automatically.
This behavior was introduced in Android 3.1 with Launch Controls:
Launch controls on stopped applications
Starting from Android 3.1, the system's package manager keeps track of applications that are in a stopped state and provides a means of controlling their launch from background processes and other applications.
Note that an application's stopped state is not the same as an Activity's stopped state. The system manages those two stopped states separately.
The platform defines two new intent flags that let a sender specify whether the Intent should be allowed to activate components in stopped application.
FLAG_INCLUDE_STOPPED_PACKAGES — Include intent filters of stopped applications in the list of potential targets to resolve against.
FLAG_EXCLUDE_STOPPED_PACKAGES — Exclude intent filters of stopped applications from the list >of potential targets.
When neither or both of these flags is defined in an intent, the default behavior is to include filters of stopped applications in the list of potential targets.
Note that the system adds FLAG_EXCLUDE_STOPPED_PACKAGES to all broadcast intents. It does this to prevent broadcasts from background services from inadvertently or unnecessarily launching components of stoppped applications. A background service or application can override this behavior by adding the FLAG_INCLUDE_STOPPED_PACKAGES flag to broadcast intents that should be allowed to activate stopped applications.
Applications are in a stopped state when they are first installed but are not yet launched and when they are manually stopped by the user (in Manage Applications).
GCM has a process running in the background, but it's a process that serves all the applkication on the device, so installing additional apps that use GCM has no effect on the number of background processes running.