Can those who fail to believe in the Son truly pray to God?
That wasn't the question. Rather, does the Triune God hear the prayers of those who do not believe in that God?
I think this has already been answered, as far as I can see. As an omniscient God one can hardly argue that God is unable to actually hear something said, whether it be in the form of a prayer or otherwise. At issue, if I'm following correctly, is whether "hear" is equated with "answer." And part of this, I submit, is how faith in the true God factors in.
It may depend on what is meant by "answer." Jesus says in Matthew 5:43-45
“You have heard that it was said, You must love your neighbor and hate your enemy. But I say to you, love your enemies and pray for those who harass you so that you will be acting as children of your Father who is in heaven. He makes the sun rise on both the evil and the good and sends rain on both the righteous and the unrighteous. [CEB]
Should a Muslim or Hindu farmer pray to their gods for rain, and God causes it to rain; is that an answer to prayer? Or is their prayers irrelevant? It was going to rain whether or not they prayed.
In these verses it seems that God treats believers and unbelievers; friends and enemies, the same - and so should we.
God watches over His creation and His decision to grant rain is not contingent on faith or the lack thereof. He does so not because a Hindu farmer prayed to a false god. He does so because of his mercy. As Luther says at the end of the explanation of the First Article: "All this He does only out of fatherly, divine goodness and mercy, without any merit or worthiness in me."
Perhaps we should reframe this question. It is clear that you and Pr. Austin believe that God hears and answers prayer whether it is offered in faith in the true God, or whether it is not. Prayers of Hindus (who pray to multiple deities), Muslims, Jews (both of whom openly deny the deity of Christ), et. al., are all valid prayers for you. Prayer is something for you, it appears, that does not require faith. Our training and theology, it would appear, are, indeed, quite different.
And if all this is true, what motivation is there to even have any kind mission outreach of the church to those who do not believe? It would seem rather irrelevant. If, in the end, they are going to be saved because of Jesus, but not necessarily because of faith in Jesus, what is the point and purpose?