Outcry is the wrong word. There'd be alot of fuss about about it if they became an item, because you'd have a black person potentially marrying into the royal family - not necessarily negativity, just fuss - like the Obama presidency. It's stupid to pretend there wouldn't.
Oooh dear - have I just revealed myself to be a racist Mark?
Some people have to define everything anyone does by their race. As she would be the first 'black princess' there would be interest, as Ludwig says, as there was when Obama ran for the presidency, but there would be no outcry from the majority of people. Only anyone with a nasty attitude to white supremacy would have a problem with her.
is she black? At a guess, I'd say Indian heritage rather than African. Anyway, Harry can date who he wants and no, I don't think there would be an outcry, except maybe in some quarters of the News section.
There's be an outcry from grandma, and that's all there needs to be. She'd stamp any relationship out before it even began if she doesn't agree with it.