In the sense that they are all working together with the same plan - no . It hasn't been like that since 1950 really (even earlier when you think of Tito).
However in the sense that all three really can't stand the US (and most of the rest of the democracies) criticising them and "meddling" (their words not mine) then yes - they have similar overall objectives which they pursue, generally, separately.
They also have issues between themselves of course - Iran is a Moslem dictatorship and the Chinese oppress Moslems, Russia and Iran are vying for influence in the Middle East, Russia and China have had their border differences over the years.
But they all are happy when they see one of the others stirring up trouble - for a start it deflects attention from their own clever tricks and secret plans