At the brunch, Metropolitan Alexios offered warm greetings and an invitation for any Metropolis of Atlanta services and programs to be also accepted as DOS services and programs.What does that mean exactly?

It means just what it says - that people are welcome to participate in any services and programs offered by the MOA, such as youth summer camp, retreats (for example, marriage & family retreats), Christian ed etc.
It's actually been going on for a long time. Metropolitan Alexios regularly invites all the Orthodox clergy of the area for Divine Liturgy, lunch and meetings. He personally invited all the Orthodox clergy and Faithful from Alabama, Tennessee, Georgia & N. & S. Carolina to attend, when the Ecumenical Patriarch visited Atlanta.
(btw, the Diocesan Assembly was held in the GOA Annunciation Cathedral for the second year in a row- at Metropolitan Alexios' invitation.)