You can only install one "application" with an APK. But you can have multiple activities defined for one Application. In your manifest.xml
you can create multiple activities, each activity can do it's own task. An application , if seen as something that performs a set of tasks that the user needs, then an activity can also be considered as an application. In that sense, when you have multiple independent activities in your application, each doing it's own task, your necessity is fulfilled.
Update: After you re-framed your question: Yes, I think it is allowed. Check out Go Launcher.Ex
Update: Article Android Launcher spam
The above article talks about whether applications that create more than one launcher icons. They have also given examples of applications. And also there are launcher spam applications that just create a load of icons in your launcher. But basically, it is very much allowed, Google does no check.
For technical details, just google how to have an application create multiple launcher icons, you'll loads of info.