Call Tag Description in Search Archive Results?

I have my tag archives setup where if a tag has a description, that description/information is called and displayed before the most recent posts are displayed in archive format. I’ve used this code to do so:

<div class="tag-description">
	<?php echo tag_description(); ?>
</div>

I was wondering if it’s possible to link search results to tag descriptions. Say for example somebody searched for the word “Tag”, could the “Tag” description be pulled from the actual tag description and displayed the same way based on the words searched?

Basically if somebody were to search and their search matched a tag, it would display the tag description above the archive.