No. The wife of a prince becomes a princess. Kate has her own title, because she is Princess William — her “princess” title derives from her husband, just as her “Duchess” title does.
True she will never be Princess Katherine … partly because her name is Catherine. She is, however, Princess William.
In rank and suffix yes. But not in prefix nor her own merit.
Pretend for a moment William was a doctor and not a prince. His title would be Dr. William Windsor, M.D.
Kate would be Mrs. Dr. William Windsor, M.D. But she would not be Dr Kate Windsor, M.D nor would she be Mrs. Dr. Kate Windsor.
She would only have the prefix of Doctor when using his first name because a prefix is granted only based on ones personal merits (birth, degrees, etc).
The suffex is the office the person holds.
A better example would be President of the United States and First Lady.
If William & Kate were Americans and William was elected President, his title would be President William Windsor, President of the United States, while Kate would be be Mrs. Catherine Windsor, First Lady of the United States.
The First Lady receives a suffix, based on her office, but does not receive the prefix President. A
prince and princess are the exact same station, a princess is not a wife of a prince, but the daughter or grand daughter of a sovereign (or great grand daughter in select situations). Same with a prince.
Note: while Kate will one day have the office of Princess of Wales, Megan will never remotely come close to being a princess because Harry will never be the Prince of Wales.
God Bless