Normally yes, but not necessarily. You mentioned implementing Dr. Bytes fix in an earlier post. Were you referring to this - referenced in post 20 in this thread?
// if no customer email record found, and admin email format is set to HTML, and sending newsletter, and admin is logged in, use HTML:
if ($customers_email_format_read->RecordCount() == 0 && ADMIN_EXTRA_EMAIL_FORMAT == 'HTML' && in_array($module, array('newsletters', 'product_notification')) && isset($_SESSION['admin_id'])) {
$customers_email_format = 'HTML';
}
If you don't have that in place, all admin emails go out as plain text.
On customer mail, I seem to remember that the default is also text.
Setting a 'FROM' email address is also of limited use unless 'Send from known domain' is also set to true, as this gets rid of 'nobody' as the mail source.
Unfortunately, that requires having a mail transport that would allow it.
At this stage I'd say ask your hosting company what mail settings they suggest to allow you to send HTML mail, and set reply to and envelope from addresses