Man in his unregenerated state will always choose to reject God
But Augustine wouldn't have agreed with that statement any more than we do. Regeneration is for him just another term for the justification that takes place in baptism. Thus Orange II: "If anyone says that just as the increase of faith so also the beginning of faith and the very desire of credulity, by which we believe in Him who justifies the impious, and by which we arrive at the regeneration of holy baptism, is not through the gift of grace, that is, through the inspiration of the Holy Spirit reforming our will from infidelity to faith, from impiety to piety, but is naturally in us, he is proved to be antagonistic to the doctrine of the Apostles ..." (Canon 5). Now here faith is clearly prior, logically and temporally, to "the regeneration of holy baptism," whereas for the Reformed regeneration precedes faith, if I understand the so-called "ordo salutis" correctly.
What is necessary for the choice of good by means of the free-will is not regeneration but a divine motion upon the will (actual grace). Augustine affirms, as the Church has defined, that the will retains some power even under the corruption of human nature after the fall: as Trent put it, "free will, attenuated as it was in its powers, and bent down, was by no means extinguished in them." Therefore God is able to guide, lead, and move a man's will to choose good even before he regenerates him: for instance, the actions which Trent enumerates as preparatory for justification: belief, fear of God, hope, love, repentance, and the intention to receive baptism and thereafter keep the commandments, these are all good although the man is not yet regenerated in baptism, nor are they not the gifts of God, accepted by a man whose will is already moved and inspired by grace. We reject both Pelagianism and Semipelagianism, the heresies Augustine fought against, and the application of his arguments against beliefs we condemn as heretical against the Catholic belief just doesn't work. "If any one saith, that without the prevenient inspiration of the Holy Ghost, and without his help, man can believe, hope, love, or be penitent as he ought, so as that the grace of Justification may be bestowed upon him; let him be anathema" (Trent, Canon 3 on Justification).
Moreover, as Augustine says: "faith itself also is found among those gifts of God which are given by the same Spirit. Both, therefore, are ours on account of the choice of the will, and yet both are given by the spirit of faith and love ..." Now, clearly he says here the faith itself is ours "on account of the choice of the will." This means that man chooses to believe. The choice to believe must be prior to belief. Therefore, for Augustine man chooses to believe before he is "instilled with God given faith"-that is, he chooses to accept God before becoming one of the faithful and before regeneration. This choice is not from him because it is given by the Holy Spirit, but it is his because he makes it freely while aided by the grace of God: ours on account of choice of the will, yet given by the spirit of faith and love. So according to Augustine it is true that "man somehow makes a choice to choose God or reject God."
Man when instilled with God given faith will always choose to accept God.
Again, this is a statement that Augustine would not have agreed to. Over and over again he impresses on his Catholic listeners and readers the fact that, despite having been justified, they can still fall from grace by the use of their free-will. Just read the Treatise on the Gift of Perseverance, the complement to the Treatise on Predestination: "But it is said, 'It is by his own fault that any one deserts the faith, when he yields and consents to the temptation which is the cause of his desertion of the faith.' Who denies it?"
Catholic doctrine would like to pretend that God gives a tiny bit of faith to everyone.
I'm not acquainted with this particular "Catholic doctrine."
Faith, then, as well in its beginning as in its completion, is God's gift; and let no one have any doubt whatever, unless he desires to resist the plainest sacred writings, that this gift is given to some, while to some it is not given. - Augustine, A Treatise on the Predestination of the Saints
Had Augustine fully thought through this truth, he would have concluded that the choice to believe must be after God gives a person faith.
While you have avoided discussing election, I would suspect you do not subscribe to Augustine's position that grace is only given to some-not all. This is not RCC teaching and what I was referring to in the last post. Instead the RCC, Orthodox, and many Protestants today, believe that God's grace is universally applied to all, contrary to scripture. I add contrary to scripture because Augustine states correctly, that it is to resist the plainest sacred writings to think otherwise.