Mark 16:16 is the Catholic teaching. You have to be baptized and believe the entirety of the Catholic Church to be saved. Extra Ecclesiam nulla salus.
The idea that God sorts out our prayer by whether Mary is in them is, however, a belief in a mean god, and is not supported by any scripture.
lol. Trying to slip that by without notice?
Include Mary in your prayers all you want. It doesn't matter. Just don't pray to Mary, but to the Triune God alone.
Idol worship is not pretty.