Can emails be sent asynchronously via rules? (Using Queue?)
Oh the joys of email. Email is sent via the servers underlying or configured MTA. PHP merely passes-off the email content to be delivered. Depending on your email configuration PHP may wait for bounce notifications for example ... or simply spool the emails to disk and wait for the MTA to flush the outgoing mail folder.

Emails from Drupal though do not need to occur on page-load or form submission. If you want you could use Rules to slowly fill a Queue (a "list") of emails to send out from the "website" periodically.

Depending on how you want to process that Queue, whether in realtime using a Process or Job/Worker library is up to you. Or you could batch up the sending of the emails using Drupal (and/or Drush) and it's built in Cron support.

Or, for instance you could use one of the many email campaign modules for Drupal such as:


Emma https://github.com/myemma/integration-emma-drupal
Mailchimp https://www.drupal.org/project/mailchimp


to completely offload the work from your server. How you wish to approach this problem, it's feasibility and cost are up to you.

EDIT:

This module works to provide Rules to fill Queues using Drupal Entities, Rules Queue. Google is your friend! :D

For some example code that uses hook_cron to send Queue'd emails:
http://www.jide.fr/english/using-rules-and-the-queue-api-to-batch-send-mass-mails