Perhaps not directly from Catacomb, as a few centuries elapsed between the end of the Catacomb culture (2000 BCE) and the start of the Mycenaean culture (1600 BCE). It's more likely that the Mycenaeans left the Steppe during the Srubna culture (1800-1200 BCE), or in the archeological vacuum in between Catacomb and Srubna. Here is what I wrote in 2009 from my first version of the R1a page (and haven't felt the need to modify since):
Little is known about the arrival of Proto-Greek speakers from the steppes. The Mycenaean culture commenced circa 1650 BCE and is clearly an imported steppe culture. The close relationship between Mycenaean and Proto-Indo-Iranian languages suggest that they split fairly late, some time between 2500 and 2000 BCE. Archeologically, Mycenaean chariots, spearheads, daggers and other bronze objects show striking similarities with the Seima-Turbino culture (c. 1900-1600 BCE) of the northern Russian forest-steppes, known for the great mobility of its nomadic warriors (Seima-Turbino sites were found as far away as Mongolia). It is therefore likely that the Mycenaean descended from Russia to Greece between 1900 and 1650 BCE, where they intermingled with the locals to create a new unique Greek culture.
Add to this the presence of R1a-Z93 and R1b-Z2103 both in the Srubna culture and in modern Greece, although apparently with a reversed frequency (R1b-Z2103 is more common than R1a-Z93 in Greece), from the scant data available for both.
So we've got archaeological, linguistic and now also genetic evidence that point to a Steppe origin of the Mycenaeans immediately after the Catacomb culture.
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