It seems to me, an uninitiated one, who didn't grow up in Ger, but did go over to Lubavitch, that I've heard these words somewhere. Something about there being a significance to the number 7, and that the 7 Rebbeyim symbolize the שבעה רועים. But it seems like that concept was publicized some time before, and that it wasn't the Rebbe who "came up with it." Ger seems to maybe have taken it one step further by proclaiming der Rebbe di Imrei Emes as Dovid Malka Meshicheh, and use his Yohrtzeit as proof. He says here in the name of the Sfas Emes that the geulah would come in the IE's time, and that if not the complete geulah then at least the Aschalta. Noted Gerrer Chossid Rav Mendel Kasher brings in his HaTekufoh Hagedolah (thank you, Dr. Balbin) that we witnessed the Aschalta with the creation of the State of Israel, היל"ת. I wonder if that stemmed from his Gerrer education, where he was taught that the IE would witness the Geulah, which he did, because he passed away one month after the creation of the State.... Chabad, however, doesn't stray from the RaMBaM in Hilchos Melochim, even if they use the Dor HaShvi'i as a sign.