Back to the original question, the answer is no. I knew and/or knew of a few students at elite colleges who did not have a high school diploma. One kid got into trouble for creating an explosion at his private school so they withheld his diploma but the college (an Ivy) still wanted him.
As for the high school graduation requirements,as long as the district approved the original coursework, there shouldn't be an impediment. Of course, your DD may be subjected to additional "assessments" and other hoops, particularly if the original coursework was not arranged with the district's blessings.
If your DD completes Calculus BC by her sophomore year, I think it is unlikely that her interest in math will then terminate. Some high schools allow/facilitate enrollment in differential equations and linear algebra. Of course, AP statistics would be invaluable in sciences and economics, etc.
