Yes, it is possible. Those applications are called IDE's. There's no special magic behind those - an IDE is just another program, albeit typically a rather big and complicated one.
That said, why would you want to do that? There are plenty of IDE's out there already. If you want an exercise, maybe something less ambitious would be a better choice.
There's no reason why your IDE should prevent the user from making GUI programs. After all, existing IDE's would let you.
Also, there are IDE's out there that are highly customizable (Eclipse and Visual Studio come to one's mind first), so if you're missing a bit of functionality, sometimes you can write/find an IDE plug-in for that.
If you don't have an IDE and want a free one, Eclipse is free. It supports Java and C++ all right. That would be much freer that creating another from scratch - time costs, too.
EDIT: I see. Now, the limitations are: small screen, lack (typically) of a hardware keyboard, limited memory, limited and slow disk, battery lifetime, overheating... App development is an expensive task.
EDIT2: looks like you're not after general purpose application development on Android, but want your app to be scriptable by end user. If that's indeed the case, C++ and Java are not the best languages to support. Android already comes with an interpreter for a scripting language - the language is JavaScript, and the interpreter is WebView.