After some extensive testing, we know that GoDaddy is compatible with the WordPress Mailing Group plugin, as of November 2014.
You cannot use the “SMTP mail” option for sending mails, but you can use the “WP Mail” or “PHP Mail” options instead under Choose Mailing Function, when you Add / Edit a Mailing Group.
One of our users was using Godaddy Windows hosted wordpress, it does not support cron. So if you are on it, switch to Linux. Thanks to Dan Tesch who gave us an account of his problem finding and resolution on GoDaddy wordpress hosting in details. Thanks to him. Read below:
Difficulties getting WordPress Mailing Group Plugin working on GoDaddy and resolution
• First, GoDaddy’s Windows hosted WordPress does not support Cron so I needed to switch to their Linux platform if I wanted regularly scheduled e-mails, I have a low volume site and did not want to use an external service to hit my site to trigger wp-cron.
• My GoDaddy account came with one of their Workspace e-mail accounts which is, I’d guess, what most people would use as this is a normal account with POP & Webmail.
o This free / included account does not support IMAP, you’d need to upgrade to get IMAP support but this doesn’t matter as you’ll see next.
• After testing over and over with SSL, no SSL, changing the ports, verifying username & password configuration was correct, etc. I tried with my personal Comcast account and a Gmail account and nothing would work so I installed the plug-in Snitch to see if I could see outgoing POP connection attempts but I could not.
• Next, I logged in via SSH to my server to see if I could ping the mail server pop.secureserver.net and I could but Telnet was not available to test further.
• Several support calls did not help because the agents did not fully understand what I was trying to do and they kept pointing me to MX record issues.
• I finally got a rep on the phone who confirmed that GoDaddy blocks POP and IMAP at some point, probably outgoing on the server but he could not explain where or how but did seemingly confirm it was blocked and there was no setting to unblock it… I thought I was done.
• That rep suggested that I could configure local mail on my server and NOT use GoDaddy’s standard mail account. I had not initially even considered this because I only use the server for WordPress and already had an included GoDaddy e-mail account. Once I configured this and confirmed it could send / receive e-mail, it was a simple matter of changing the incoming Mail Server name to localhost or the hostname of my server.
o This got things working but only on 110, SSL / 995 does not appear to work but I’m not too concerned about it because the communication is only local and not over a public network.
I hope this helps someone else either with GoDaddy or another hosting provider, I couldn’t find an answer on Google and was becoming very frustrated. GoDaddy’s support agents are generally pretty good but on this particular issue, they were just not understanding what I was trying to accomplish.