In reply to:
I was wondering if there was an email limit for sending out emails from the server email account.
From Question #49 of 116 Common Questions - DH wiki Article
In reply to:
Do you allow mailing lists to be sent out from your servers? What is the email per hour limit?
You should use our mailing list software for any mailing lists you want to run with us. Websites that send email are limited to 100/hr via SMTP and 200/hr via SSH/SHELL. All mailings must be compliant with our anti-spam policy.
Note that even "sending newsletters for an organization", *must* be done in compliance with DH Anti-Spam policies, or you are likely to have problems. They are *very* precise in their requirements, and you should review them carefully before sending *any* mass email, even if you think you have a valid "opt-in" list - if you fail to do this, you will probably find that you are *not* in compliance. 
--rlparker