If they could act in a manner that didn't go against the character type, I think it would work.
This means the stereotypical cool-attitude that usually accompanies african american actors who play a heroic role, would not suit it.
A superman acting all cool-black-toughguy, like shaft or the hero's from bad boys, just wouldn't work.
Lawrence Fishburne, as Morpheus in The Matrix, played the character in a way that did not portray the stereotypical black-attitude. It's that sort of acting I feel that would be necessary to make it work.
I think the more mediocre-neutrality that usually stereotypes a caucasian character is generally what is needed for most super hero roles. Their secret identity is usually a mild mannered, everyday type person, or a fairly discrete person despite their success. Even the rich and socialitic alter-identities, such as Bruce Wayne or Tony Stark, are more just flambouyant in their spending of money and dry humour, rather than typically loud or memorable in terms of character, and they usually had their weaknesses of character. The stereotypical black-attitude is more wet humour, very cool and proud, generally devoid of a weakness.
If a black actor could do one of the known superheros in the same dry manner, with a weakness of character people could relate to, I think it would work. But in the same sense, this could be changing the black stereotype to a more white stereotype, which may make it less easy for black people to relate to.
Perhaps these superhero characters just portray a typically caucasian stereotype.
I think if there were to become a new unique superhero, flambouyant and cool in the black stereotype sense, it could work also. The alter ego could be a rich personality, a black rapper or sports person. This could set up a believable reason for the alter ego's fortune.
What about a black boxer who fights crime on the side?
This might fail simply because a black rapper or sports personality is generally quite proud and self-promoting to begin with, so making a superhero of them might be just too much elevating of the character, but then again, thats generally where portraying a weakness in the character becomes effective.
Will Smith in Hancock, and Robert Townsend in Meteor Man, both do a superman role, but it's done rather satirically and more pokes fun at the role. Meteor Man is a good recommendation to watch tho, regarding this topic, as it pretty much was made in an attempt to ask the very same question, Can a black man play superman?