To echo 33Girl's earlier post: No NPC sorority has a national brother fraternity. Most if not all NPC sororities do not support their chapters adopting a local brother fraternity.
Locally, there was a time when university Greek Systems adopted auxilary groups within GLOS-- Big Brothers, Little Sisters, etc. We no longer do this.
Several of these traditions still take place on local campuses. They go unrecognized by NPC, campus Panhellenic and the chapters as official groups.
I have heard the rumor about ADPi and SAE. While we share some symbols in common, it is just a coincidence.
At UCF, we pair up with a fraternity each homecoming, and another for Greek Week. We call each other our "Homecoming Partners" or "Greek Week Buddies."
There used to be events like King of Diamonds, etc., but for the most part chapters don't hold these contests because ADPi doesn't wish to mistake that we are anything but a women's organization-- men don't represent our letters as auxilary members.
ADPi does have a signature philanthropy event that can be adapted to each chapter. It is called the Lion's Share Challenge and the chapters have the freedom to work within this event to make it unique to their campus as a sporting event, dance-off, fundraiser, etc.
The reasons for not having a big bro/lil sis have to do (again!) with insurance and maintaining status as single-sex organizations. I'd hate to open sorority recruitment up to a man... Imagine him at the new member sleepover. Pillowfight, anyone?