No, that's not really possible because page plugins are only supposed to define the content of the page, not the look. In fact they run before the theme is even initialised (see the bottom of qa-page.php).
The opposite is possible however - if you've modified something in the $qa_content array in your plugin, that will be available in the theme. So depending on what your variable is, that could work.
Your best bet might be an option that you retrieve in both the page plugin and theme using qa_opt().