No. There is no reason for Meghan, Duchess of Sussex, to lose her American accent. Many foreigners have married Brits and kept their native accents. Queen Alexandra, consort of Edward VI, kept her Danish accent. Prince Albert, consort of Victoria, kept his native accent and his British-born son, Edward VI, had a slight guttural glide to pronunciations of specific letters.
It is a natural occurrence for some people to pick up the accent they hear after many years of living in a certain place; perhaps this will happen with Meghan Sussex. What will happen, in regards to language, is that she will pick up on phraseology, wording of the British people in order to be able to communicate clearly.
The wording for the answer should be Yes or No. True means that a choice is proven to be correct, while false means that a choice is proven to be wrong. There is no right or wrong for this answer. You are asking people for their opinions of whether Meghan should or should not change her accent.