Sorry for the delay in replying...
Sure, this is possible to add
Sources/shop/Shop-Buy.php, find:
case 3:
$context['shop_inv']['sort_type'] = $txt['shop_stock'];
$sortQuery = 'stock';
Add after:
case 4:
$context['shop_inv']['sort_type'] = 'Date added';
$sortQuery = 'id';
Themes/default/Shop.template.php, find:
<option value="3"', ($context['shop_inv']['sort_type'] == $txt['shop_stock'] ? ' selected="selected"' : ''), '>', $txt['shop_stock'], '</option>
Add after:
<option value="4"', ($context['shop_inv']['sort_type'] == 'Date added' ? ' selected="selected"' : ''), '>Date added</option>
This will add a "date added" option to the sort box on the buy items page. If you want to call it something else, change "date added" to whatever you want to call it (it occurs three times in the above code sections)