Chris,
I’m afraid that the way our search module operates, that wouldn’t be possible in the manner you describe. The search module runs the query, caches the results, and returns a token to that cache to the results page for better performance. You could likely do something similar to this however:
{exp:search:simple_form channel="news"}
<input type=“hidden" name="keywords" id="keywords" value="{gallery_keywords}" />
<input type="submit" value="submit" class="submit" />
{/exp:search:simple_form}
You could use some javascript to make a link to submit the form, and the {gallery_keywords} variable would need to contain words separated by a space, but it should work.
Cheers,