That really sounds like a cop-out to me. If I ask any skeptical question about the Biblical God's morality, why would God's answer be, that he can do whatever he wants because he is God (Like the verse you quoted), and to just believe him ("You, being a fallible sinner, have no right to judge God's plan; you are called to have faith in Him.")? It doesn't make sense when it's just stating that God can do whatever he wants, which is true, but it doesn't explain why the things he did are acceptable. If there really is an explanation as to how God's plan is completely just (God would obviously have one), then why didn't God lay out why the things that he did are just in an understandable way, instead of just saying "Don't question me because I'm God."? Why can't we question God if God has an answer? The answer to that is that the author of Romans (Paul) has no answer, so "God" doesn't either. Your answer to the point I'm making right now could just be that I'm not one to question God in the first place, but that would just bring me to repeat this same point. And if your answer would bring me to repeat myself, your answer wouldn't have addressed my point in the first place.
The answer that the creation cannot judge the creator only works for people who already are Christians, as a reason to not doubt God, because they are viewing the point from within Christianity, but to give that answer to a non-believer wouldn't work, because from the outside looking in, it looks like a cop-out. So if whether or not someone thinks the argument is valid is subjective to someone's pre-existing views, instead of the logic of the argument itself, the argument is completely useless as an explanation to give to a non-believer, making it a bad answer to the point I made, and a bad answer for a Christians to give themselves. If you're going to say that I just don't see it (how the Biblical God can be all-good and impartial because of the way he went about his plan), are you implying that you do see it? If you do, do you know of any way that you could explain it to me in a way that you don't already have to believe the Bible to accept that the point is true?