Hey Aspire,
I went to a rush before for Delta Sigma Theta and they made it CLEAR that they aren't the second choice for anyone, and if you applied for another NPHC org than you cannot apply for them. I'm so sorry for the bad news.
BUT every chapter and campus is different and I'm not a member of any org just a fellow Sister Friend.
. So try it out anyway you'll never know.
Good Luck
K