They are formerly the Free Russian Orthodox Church (I do not understand the name transition - mayhaps someone else can explain this) that was secretly a church while the USSR existed as the MP was fully Sergianist. They are currently in communion with the GOC (Genuine Orthodox Christians of Greece & the Diaspora) I believe, as the GOC approves their books. A ROCOR bishop has also decreed their books edifying reading for the soul and without error.
But no, they are not in communion with World Orthodoxy. Their problem with ROCOR is that they are in communion with the True [Old Calendarist] Orthodox Church of Greece that the GOC and ROAC see as Ecumenical.
Umm hope this helps and does not confuse you more. A ROAC person is currently posting at the Cafe if you want to ask her.