<p>It seems <a href="http://openlaszlo.org/" rel="nofollow noreferrer">OpenLaszlo</a> can <a href="http://www.antunkarlovac.com/blog/2008/02/19/writing-an-openlaszlo-air-application/" rel="nofollow noreferrer">run on AIR</a>. What's less obvious is whether OpenLaszlo apps can use the AIR-specific APIs, like file system access. If so, how exactly is this done?</p>

While I don't have any specifics, the article you linked mentions that his application window can be dragged and closed. Those are AIR-only APIs (see the NativeWindow class), so presumably what you're asking about must be possible to some extent.
However, my understanding is that OpenLaszlo tries not to implement things that can be done in Flash but not (say) DHTML, so it may be less obvious how to do things like local file access. Probably you'll want to download the source linked in the article and see how he implemented the window drag/close.