Can Armenian and Greek IE language lineages be on the same branch?

I've generally seen where Armenian is considered Satemized whereas Greek is not. However, I've now read that there are proposals that Armenian is not Satemized but did quite a bit of borrowing of Indo-Iranian languages. I've also seen computational cladistic runs that place Armenian and Greek on the same branch that was called Hellenic and that branch broke away right before the full Satemization completed leading to the Balto-Slavic and Indo-Iranian dialects.

Is there a good case that Armenian and Greek predecessors are of the same branch?

The reason I ask is this would align with some genetic results found in population studies about the types of Y chromosomes found in Greek and Armenian populations and also along the western coast of the Black Sea.

------ WIKIPEDIA EXCERPTS ON ARMENIAN AND GREEK ---------
The hypothetical Proto-Graeco-Armenian stage would need to date to the 3rd millennium BC, only barely differentiated from either late PIE or Graeco-Armeno-Aryan.
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Proto-Greek would have been spoken in the late 3rd millennium BC, most probably in the Balkans
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Close similarities between Ancient Greek and Vedic Sanskrit suggest that both Proto-Greek and Proto-Indo-Iranian were still quite similar to either late Proto-Indo-European, which would place the latter somewhere in the late 4th millennium BC
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Greek is a Centum language, which would place a possible Graeco-Aryan protolanguage before Satemization, making it identical to late PIE. Proto-Greek does appear to have been affected by the general trend of palatalization characteristic of the Satem group, evidenced for
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Armenian shares a number of major innovations with Greek, and some linguists group these two languages together with Phrygian and the Indo-Iranian family into a higher-level subgroup of Indo-European which is defined by such shared innovations as the augment. More recently, others have proposed a Balkan grouping including Greek, Armenian, Phrygian and Albanian.
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The large percentage of loans from Iranian languages initially led linguists to erroneously classify Armenian as an Iranian language. The distinctness of Armenian was only recognized when Hübschmann (1875)[7] used the comparative method to distinguish two layers of Iranian loans from the older Armenian vocabulary.
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In his paper, "Hurro-Urartian Borrowings in Old Armenian", Soviet linguist Igor Mikhailovich Diakonov notes the presence in Old Armenian of what he calls a Caucasian substratum, identified by earlier scholars, consisting of loans from the Kartvelian and Northeast Caucasian languages such as Udi. Noting that the Hurro-Urartian peoples inhabited the Armenian homeland in the second millennium BC, Diakonov identifies in Armenian a Hurro-Urartian substratum of social, cultural, and zoological and biological terms such as ałaxin ('slavegirl') and xnjor ('apple(tree)'). Some of the terms he gives admittedly have an Akkadian or Sumerian provenance, but he suggests they were borrowed through Hurrian or Urartu. Given that these borrowings do not undergo sound changes characteristic of the development of Armenian from Proto-Indo-European, he dates their borrowing to a time before the written record but after the Proto-Armenian language stage.
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Regards,
Mike W