Is there a noticeable difference in cake making between AP flour and unbleached AP flour?

Both. They have different uses.

Bleached flour is a little better for cakes, that's why you see most cake flours bleached. King Arthur makes an unbleached cake flour, and they admit that the cake might be heavier or more coarse. The cake bible explains this better.

Rose Levy Berenbaum has an interesting blog called The Power of Flour. Through food science research and her own experimentation she has shown that bleached flour works better in high ratio cakes because it can carry and distribute the extra fat, sugar and liquid contained in these recipes. The resulting cake will not sink in the center as the same cake made with unbleached flour. The bleaching process alters the surface of the proteins in the flour which result in improved baking properties.

Freshly milled flour makes a sticky dough and products with less volume than those made with aged flour. There's actually a natural oxidation process for flour during which it turns whiter if allowed allowed to rest for several weeks after milling.

But, because time is money, in the US, chemicals are used to expedite the "bleaching," including potassium bromate and chlorine dioxide, to rapidly "age" flour, to make it whiter, and to give it better absorption qualities.

In Europe, most of those additives are banned. They let the flour sit in the air for a week or two, to bleach naturally, without chlorine, bromates and peroxides, since some of them are considered carcinogenic.

I haven't been brave enough to try unbleached flours on cakes...they won't be as soft and fluffy, I think. I have tried unbleached flours on bread and for that they've been fine.

This thread got me thinking. I made a cupcake recipe recently and it was good, but the texture wasn't as soft, it was a bit more coarse. Then I realized that I had switched to unbleached flour, which works great in everything else, but did make a slight difference in the cupcake. Since all I have for bleached flour is cake flour, I'm going to make that recipe again today to see the difference.

While unbleached didn't ruin the recipe, I did notice a difference. In cookies and quick breads there really isn't a noticeable difference.

I'll bet many of us can think back to certain things that failed and we couldn't figure out why. I still prefer unbleached flour but at least I understand its limitations.