anything is possible, however how much time and effort do you want to invest in it?
in this ccode of the #header div in header.php:
<div id="header"><?php if ($himg = sdstheme_header_image()) { ?>
<div id="header-image">
<h1 id="blog-title"><span><a href="<?php bloginfo('home') ?>/" title="<?php echo wp_specialchars( get_bloginfo('name'), 1 ) ?>" rel="home"><img src="<?php echo $himg ?>" alt="<?php bloginfo('name') ?>" /></a></span></h1>
</div>
<?php } else { ?>
<div id="header-text">
<h1 id="blog-title"><span><a href="<?php bloginfo('home') ?>/" title="<?php echo wp_specialchars( get_bloginfo('name'), 1 ) ?>" rel="home"><?php bloginfo('name') ?></a></span></h1>
<div id="blog-description"><?php bloginfo('description') ?></div>
</div>
<?php } ?></div><!-- #header -->
as you can see, there is a conditional query, if you use an image or not, and with image is does not show the title and description.
you could try and remove your header image again to get title and tagline back, and then add your header image as background to the style.css #header-text:
#header-text {
padding: 1em;
background: #123456 url(images/yourheaderimage.jpg) center top no-repeat;
}