Not at all; the Mountbatten-Windsor family has at least one other strain of African ancestry, a product of the quite remarkable life and times of General Abram Gannibal, a former slave who was probably born somewhere to the south of Lake Chad in about 1696.

Gannibal was seized by slavers when he was about seven years old, and ended up in Constantinople, where he was purchased by a member of the Russian diplomatic legation there and sent to St Petersburg as an exotic gift for Peter the Great. The Tsar took a liking to the boy, freed him, stood godfather to him and had him well educated. Entering the Russian army, Gannibal became a noted engineer and was responsible for many of the line of forts built to demarcate Russia's border with China.

In the course of a long career, Gannibal married twice; one great-grandson was the poet Pushkin, who compiled a biography of his ancestor and used him as the model for a "Moorish" character in an unfinished novel.

Pushkin's daughter Natalie married Prince Nicholas of Nassau in 1868 and became Countess of Merenberg. Their daughter, Sophia, became the wife of Grand Duke Mikhail of Russia and in her turn also had a daughter, Nadjeda, who married George Battenberg, Marquess of Milford Haven – who was the grandson of Queen Victoria – in the Chapel Royal at Buckingham Palace in November 1916.

The Battenbergs - who changed their name to Mountbatten thanks to the anti-German hysteria that raged at the start of World War I – attracted a fair bit of press attention at the time of the wedding, and Nadejda's descent from Gannibal was sufficiently well known for there to have been snide and racist speculation at the time as to the likely colour of the couple's offspring.

As Marchioness of Milford Haven, Nadejda became Prince Philip's aunt, and hence Prince Harry's great great aunt. Her relationship with Philip was a pretty close one; she acted as his stepmother for a while during his adolescence when his exiled parents, Prince and Princess Andrew of Greece, sent him to be educated in Britain.

The rest, as they say, is history.

Source

Hugh Barnes, Gannibal: the Moor of Petersburg (2005)

Predating the 'House of Windsor', but still part of that familial line, there is a controversial theory that the wife of King George III, Charlotte of Mecklenburg-Strelitz (1744-1818), may have had African ancestry. The main proponent of the theory is a historian named Mario de Valdes y Cocom, who argues that Queen Charlotte had pronounced 'Black' facial features, and that this can explained by her descent from, ultimately, King Alfonso III of Portugal (1210-79) and his possibly Moorish mistress, Madragana. Apart from the extremely problematic aspect of framing specific types of facial features as inherently Black, the theory ignores the fact that something like 15 generations sit between Charlotte and her possibly-black forebear, and than numerous other European royals could claim the same point of ancestry without being perceived as Black. I can't think of another mainstream historian who regards the theory as credible.