Sure, you could try this:
function searchCallback(html) {
var html_hidden = $('<div style="display:none;" class="hidden_insert">'+html+'</div>');
$('#divSearchResults').html(html);
$('#divSearchResults .hidden_insert').slideDown('medium');
}
Not the prettiest thing but it would work. You could pretty it up by making a CSS style for the class 'hidden_insert' that would make a element with that class hidden by default. Also, on your backend, where you are sending this date from, you could do the wrapping there instead of in your javascript. The script could then be simplified to something like:
function searchCallback(html) {
$('#divSearchResults').html(html).find('.hidden_insert').slideDown('medium');
}
I haven't tested either of these but they should work.