The
NOVA tournament Doubles does the following in terms of allies:
"Any two combined Doubles Lists created from codices not referenced as Battle Brothers on Page 113
of the
40k Rulebook are instead treated as Allies of Convenience in all cases."
http://www.novaopen.com/wp-content/uploads/2015-40K-Trios-Draft-Primer1.pdf
So it looks like "Come the Apocalypse" allies are treated as "Allies of Convenience" in that case. However, even if you go with that ruling I don't believe it allows you to share Psychic Powers.
I don't play in tournaments myself mind you... this is just some quick Googling on my behalf for you.