I have not checked to see if there are any hooks into the core shortcodes. You could copy the caption code to make your own, adding any functionality you want.
Like here: http://wordpress.org/support/topic/add-new-caption-shortcode-attribute?replies=8
I have tried these codes:
[caption id="" align="alignleft" width="160" caption="Gaye Holud"]<img title=”Gaye Holud” src=”http://www.mcat-prep-test.com/photo-gallery/gaye-holud.jpg” alt=”Gaye Holud” width=”160″ height=”80″ />[/caption]
When I update the page, the codes get changed to this:
<div class=”mceTemp”><dl id=”” class=”wp-caption alignleft” style=”width: 170px;”><dt class=”wp-caption-dt”><img title=”Gaye Holud” src=”http://www.mcat-prep-test.com/photo-gallery/gaye-holud.jpg” alt=”Gaye Holud” width=”160″ height=”80″ /></dt><dd class=”wp-caption-dd”></dd></dl></div>
http://www.mcat-prep-test.com/video-gallery/
Are you using the “HTML” tab in the editor and not the “Visual”? If you are using the “Visual” tab – try switching to the “HTML” tab and then pasting in the code above.
WordPress captions do not natively support HTML, so your hyperlinks would be stripped out. There’s this plugin:
http://wordpress.org/extend/plugins/links-in-captions/