kurt vonnegut said:
I'm sure that some would and some would not. But, maybe more importantly (since there are more of them), A lot of Muslims and Jews and Hindus and other people would be brought to the 'correct' teachings. From your perspective, it isn't just the atheists that are in error.
I don't fully know how I would personally respond God showing up and laying out the truth. I have far more objections to religious institutions than I do to Jesus himself - meaning that I think that I admire a lot about Jesus and I fail to see the things I admire about Jesus in much of modern Christianity. So . . . . whether I would fall to my knees and follow God kinda depends on what is being presented. I think that is a fair answer if Christians believe we are asked to follow God and choose God rather than follow authority blindly.
One thing is for certain though - we would all be able to make better informed decisions. Consider an analogy of a dating couple versus an old married couple. A dating couple may say they love each other and they may choose each other and trust each other even though they haven't known each other very long. A couple that has been married for decades may decide to love each other and trust each other even though they know all of the short comings and flaws of the other person. Not saying that God has flaws . . . . only that better knowledge of someone allows for a deeper more meaningful love and relationship. My wife has seen me at low points and still chooses me. That means more than the fact that she choose me before those low points.
This question can be turned around also. If Allah showed up today and proved beyond all reasonable doubt that the [insert your Islamic tradition of choice] is the true faith, would Christians follow all prescribed moral laws? Probably some would and some would not for similar reasons. People of all types can be stubborn.
To your first paragraph, that's why we have the doctrine of "invincible ignorance". Just because someone has not heard of Jesus doesn't auto-deny them eternity with God. There are church fathers going back to the 2nd century talking about how some of even the Greek philosophers were "Christian" before Christ was even born. Each is asked to act in accordance with what he has received. So your "subjective experience" concern can be met with "subjective judgement" in a way, because only God knows the heart of each individual.
I like your marriage analogy and would like to build upon that. The old couple only has the benefit of more fully loving each other because they took the plunge to intertwine their lives. Those marriage vows are an act of faith in the other. No one really knows all the issues that their new spouse may or may not be hiding, or what they may or may not choose in the future. Faith in God isn't really that much more of a reach than faith in a successful marriage when you really consider all the variables.
Yes, if Allah showed up today and offered irrefutable proof that Islam was the one true religion, I would follow. If He is the maker of the entire universe, it stands to reason He is going to have a really solid understanding of what we're made for. I'm as close to 100% confident as I can be that it would never happen, as Quran says the Bible is uncorrupted. The same Bible that shows Islam to be false because it calls Jesus God and says He established a Church to be followed by all believers. I don't see a reality in which God tells me a 4 sided circle exists, so I'm pretty sure I don't have to worry about that issues.
ETA: to the part about Christians choosing to follow God: yes, we do. But I think all but the most saintly of Christians would say that choice includes being beholden to some moral demands most would rather not be held to. The only thing God is "presenting" would be the knowledge that He created the entire universe and knows what's best. You either assent to that or say that you're smarter/better than the Creator Himself.