Is it possible to add normal text (i.e. not links) to the top of my EZ-Pages sidebox?

It certainly is.

To insert the text, we firstly create some over-ride files. If it doesn't already exist, create the following directory

    includes/templates/YOUR_TEMPLATE_NAME/sideboxes

and copy includes/templates/template_default/sideboxes/tpl_ezpages.php into it. Similarly, if they don't already exist, create an

     includes/languages/YOUR_LANGUAGE/extra_definitions/YOUR_TEMPLATE_NAME

directory for each language you are using and copy includes/languages/YOUR_LANGUAGE/extra_definitions/ez_pages_definitions.php into them.

Now let's create the text for insertion. Open each of the ez_pages_definitions.php files that you just created and insert the following define statement in the appropriate language
define('BOX_TEXT_EZPAGES', 'The text you want to insert into your EZ-Pages sidebox');
This doesn't have to be plain text. If you wish, it can be any string of HTML.

Next we tell the EZ-Page sidebox to use the text. Open the copy that you made of tpl_ezpages.php and insert the line marked below
 $content = "";
 $content .= '<div id="' . str_replace('_', '-', $box_id . 'Content') . '" class="sideBoxContent">';
 $content .= BOX_TEXT_EZPAGES;  <----- this is the line that you insert
 $content  .= "\n" . '<ul style="margin: 0; padding: 0; list-style-type: none;">' . "\n";
Finally, upload the new files to your server and check the results in your browser.