Not in my opinion, due to the fact that the Greek-Latin schism results from the disintegration of a unified state (Roman Empire) while the US/Russian rivalry is the result of the conflict of two distinct states which have never been united unless it was against an enemy the world was united against (Hitler, modern islamic extremism). The Greek-Latin Schism was also haphazardly mended at times (Justinain Reconquests) while there was no period of amicable relations between the US and Russians at all during their history since right after the US exited its isolationist state, it was during the Cold War. Lastly there's the fact that both the Greeks and Latins learned from and adopted styles from one another while the US and Russians have remained distinct units and, if anything, it was the imposition of US culture due to its dominance and not a two-way cultural exchange like the Greeks and Latins.