yes i think it can be done
you must edit the index.php of the template and put some code in there afther the image of the logo that can load the module
you can create a new module name in the backend and the publish the module of the banner in this new created module
im no joomla template expert but i think you can do it
you are planning to erase the date of the top of the template to place ther the banners module
hope this help
<!-- BEGIN: HEADER -->
<div id="ja-headerwrap">
<div id="ja-header" class="clearfix">
<h1>
<a href="index.php">
<img src="<?php echo $ja_template_path;?>/images/logo.gif" alt="<?php echo $mosConfig_sitename?>" />
</a>
</h1>
<div class="ja-banner">
<?php mosLoadModules ( "new011", -1 ); ?>
<div class="ja-day">
<?php
echo "<span>".date ('l')."</span>";
echo " <div>".date ('M')." ".date ('d').date ('S')."</div>";
?>
</div>
</div>
</div>
</div>
<!-- END: HEADER -->
This code will show you the logo the date and the banner where NEW011 have to be the name of the new created module in the backend.
You have to code better the css in order that this fit your needs
Is only my raw solution to this and it seems to work but is no the oficial solution becouse it have to be more well treated in the css in order thay all fit well
hope it helps