Craft Commerce: No Emails sent on Default Order Status
I just tested this with a default Craft Commerce installation, assigned an email to the default "Processing" order status, placed an order and received the email as expected.

I'd double check under Settings-&gt;Email in the Craft control panel you're not using phpmail or sendmail and you're using a proper SMTP server or transactional email provider like Mailgun or Mandrill, etc.  The others are notoriously unreliable at delivering email.  See: https://craftcms.com/support/troubleshooting-email-errors#dealing-with-email-delivery-issues