The fact that DBZ doesn't have that much depth in their character creation really works for you.

In my viewpoint, the problem comes if you assume your readers should know the plot of the manga, in which case you're burning the "fanfic"-brand on the story. If you have a way of explaining the history (possibly in a creative, original way), you could breach away a little.

How about names? Are you using Toriyama's names for the DBZ character's and places?