I've done it for the last 3 seasons, maybe it's not textbook ripening, but it definitely evolves towards a more edible/enjoyable fruit. It's like bananas. In fact, don't we refer to bananas "ripening" as the sit on the counter and go from the green, tongue-coating starchy experience to the yellow, sweet and soft fruit we prefer to eat? Then, they become "over-ripe" once they start going black and mushy (which, I actually prefer, up to a certain point). If I cut that Sweet Tart up now and eat it, it'll be all sour, chalk & starch. Given time, those starches breakdown/convert to sugars and the texture softens to become much more enjoyable. I bet in a week or two, I'll enjoy eating this fruit.
I don't enjoy a wealth of quality mangoes in my area, gotta make do.