Hi,
It should yes.
Try adding the line:
.hikashop_product_variant_subname{ display:none !important; }
in the popup of the edit button of the "template" setting of the email.
Also, can you check what you get for that email in the Customers>Emails history ?
It's possible that it will display as expected there and that the problem comes from your email client blocking that CSS command.
In that case, a more invasive solution would be to change the line:
$t = '<p>' . $item->order_product_name;
to:
$t = '<p>' . preg_replace("#<span class=\"hikashop_product_variant_subname\">(.*?)</span>#is", "",$item->order_product_name);
in the "preload" section of the email (bottom of the edit page).
That will strip the HTML from the product name.