Are bananas edible once portions of their skin turn brown or black?

Yes. Fact is, many consumers prefer the sweet taste and mushy texture of blackening or "overripe" bananas.  However, excessive blackening may denote the onset of spoilage. It also may simply denote the bananas were refrigerated. The skins of refrigerated bananas blacken quickly, though the underlying fruit generally remains edible for several days. 
 
Because skin color isn't  always an accurate indicator of spoilage, look for other signs such as a bitter flavor, “off” odor, and/or mushy texture.
 
Source(s):
Gallimaufree.wordpress.com "Dealing With Barely Edible Food"
Banana.com "How to Purchase"