It wouldn't necessarily matter if they send mail or not. If their servers are misconfigured or open relay, they could be listed in an RBL (check ordb.org also) and certain hosts/ISPs will use such as RBL for filtering on their networks.
Just as it was last time - ATT blackholed all traffic going to the two blocked redirectors at the request of comcast due to an apparent phishing site being redirected - which of course resolved out to one of those IPs - so they blocked access to the entire server.
This is the same thing that happened last time they blocked access, and does have nothing to do with relays, sorbs, rbl, or anything else of that sort. problem is resolved though.
I don't know whether this is coincidence or caused by the above stated problem:
For at least a few minutes that I know about Sunday May 1 my .org domain registered through Namecheap (Enom reseller) and set to redirect to my Godaddy-hosted .com was failing to redirect. After rechecking several times it got better, and it now works. My .net also registered with Namecheap and set to redirect to my .com did not malfunction during the time I checked it.
My internet access that I use to check is AT&T Worldnet. Also Godaddy gets the internet connection used to host the site from AT&T.