Is there a way to find out how long a single-loop animated GIF will take to finish?
Well, the specifics sorta depends on what interface you're using to manipulate those animated GIFs (I'm not aware of a real slick way in native Java/AWT/Swing), however the basic idea would to calculate (frame rate * number of frames).
If you're coding a GIF manipulation tool by hand, I recommend taking a look at http://www.onicos.com/staff/iz/formats/gif.html
Hope this helps at least a little.
Update: Try implement the ImageObserver interface. Take a look at the ImageObserver.FRAMEBITS flag in that class to detect frame updates. http://docs.oracle.com/javase/6/docs/api/java/awt/image/ImageObserver.html
This still leaves the question of how many frames the gif has. You might want to try taking a look at the Image.getProperty() function. I'm having some difficulty finding documentation as to whether there's a "frame" property, but take a look.