When you say that- do you mean to launch another application?
Supposedly open() will launch an application of the specified parameter, but it doesn't seem to work very well.
link() successfully opens a web browser to a link, but it starts another one every time...
If you use a straight Java library then it is definitely possible.

Sorry, re-reading my question I realize I didn't divulge enough information to explain what I meant.

I mean to display and manipulate an application window within Processing.

So say, launch an application and then map the application's window to one of the faces of a cube, and display this as the Processing sketch.

I think it is possible to window capture another application as long as it is allowed for safety reasons.
You would need to use a lot of Java, though.
Maybe look at this tutorial (I think the first example said something about capturing the output of an external application), see if it's useful.

I think this is rather difficult, especially from Java. There is the AWT Robot class which lets you take screenshots from a Java application / Processing sketch. It is not that hard to use, but also not very fast...