Just tested it in InfoPath 2010 Filler and no luck.
I found the TaskPanes collection and TaskPane object but no width property.
The CurrentView.Window has a width property but it does not affect the remaining width of the application window.
Even tried Javascript from the task pane, still no luck.
After a bit more Googling, ended up here http://blogs.3sharp.com/davidg/archive/2008/01/23/4668.aspx, which was great to learn how to change the URL of the loaded file but still no width.
Microsoft? Clearly giving us a hard coded 187px wide task pane is not enough.