I have set up an unused Macbook Pro as a shared server on our internal company intranet. I'm kind of running it as a skunkworks; it can access the internet, but doesn't have permission to access, say, Gmail via SMTP. It's also unlikely to get that access anytime soon.
I'd like to be able to run processes on the machine that send notification emails. Every library I can find seems to require an email server, and I can't access one.
Is there any way to set up my MBP to act as its own email server? Thanks.
adding this an answer cause not enough space in comments. 
It might work, but highly unlikely, and if you can send outbound mail, it will most likely be spam folder'd or dropped.  The reason most apps use a dedicated mail server or smart host is that there are lots of other things that need to be setup besides the mail server (DNS records, SPF, DKIM,etc..). By default it if type sendmail user@example.com on your mac, type your message and end it with a . on a line by itself you mac will try to deliver it using its internal server(postfix). It will look up the Right Hand Side, look for MX records,  try to connect to port 25 on the lowest order mx, and do all the things that a mail server does when delivering email. But if your skunk work project cannot access gmail on port 465 or 587 due to firewall settings, then there is very little chance that your mail admins will allow it to connect to random servers on port 25 (since this is exactly what Direct to MX Bots/Malware do).   
You best bet is to contact your admins and tell them you have an application that needs to send email, (low volume, notification type, whatever), and ask them if they have an approved server that you can smart host via. 
Going around network security, even with the best of intentions, is generally a bad idea.  Since the rules are generally put in place for a reason
How can I send mail via Python on Yosemite... without an outside server?