History suggests otherwise.

As for the other questions, I do not think the Soviets did a mistake by doing that, and Cuba and Venezuela are already working within that framework of "alliance", for better or for worse.

On the other hand, if you want to join the CPC you must be atheist, and Lenin seemingly agreed with that position:

The CPC also wrote a longer text about religion, which I personally haven't yet read, but you might be interested in it. https://redsails.org/on-the-question-of-religion/

I believe that studying how other Marxist groups/parties dealt with religion can be insightful for us (and I'm a militant anti-theist).

I do not think that the Catholic church can be revolutionary, actually I believe they will always remain reactionary and will keep defending private property. If anything, catholic workers can be revolutionary, but not the church itself.

Also Pope Pius XII explicitly excommunicated communists in 1949 lol