<div class="error-display" id="sku-upc-error"></div>
You can, here is a neat little trick.
When you add the line breaks, add a class to them like so...
$('#sku-upc-error').html(jqXHR.responseText).before("<br class='break' />");
Then when you run the code to hide the error message, include this code directly after it to remove the line breaks.
Give that a try and let me know how you get on. You can also use
.hide() if you wanted but this removes them all from the DOM properly rather than hiding them but keeping them within the markup.