No he could have married and remained King in theory. See
en.wikipedia.org/wiki/Abdication_Crisis_of_Edward_VIII
As a result of these rumours, the belief strengthened among the British establishment that Wallis could not become a royal consort. The government of
Stanley Baldwin explicitly informed King Edward VIII that it was opposed to him marrying Mrs. Simpson, indicating that if he did, in direct contravention of their advice, the Government would resign
en masse. Under pressure from the King, Baldwin (who knew what the answer would be), agreed to suggest three options to the King’s many prime ministers in his other kingdoms throughout the
British Commonwealth. These were that:
*]they marry and Mrs Simpson become Queen (a “royal marriage”)
*]they marry and she not become Queen but receive some courtesy title instead (a “morganatic marriage”)
*]he abdicate to marry Mrs Simpson.
The second option had European precedents (for example, Austria’s heir to the throne, Archduke Franz Ferdinand - whose assassination in 1914 triggered off World War I) but no parallel in British constitutional history. The Commonwealth’s prime ministers were consulted, and all but one—Eamon de Valera of Ireland, who argued for the first option, on the basis that as divorce was legal, King Edward should be allowed to marry a divorcée—agreed that marriage to Mrs. Simpson in any form was not an option they would accept.
Also see news.bbc.co.uk/2/hi/uk_news/2707489.stm
chilit.org/HERMANN1.HTM
This paper examines the Abdication Crisis of 1936 resulting from King Edward VIII’s decision to marry Wallis Simpson. The paper argues that instead of requesting the passage of legislation authorizing a morganatic marriage between the King and Mrs. Simpson, the monarch could have sought public support for his marriage with favorable press coverage from sympathetic newspaper owners such as Lord Beaverbrook and Lord Rothermore. Instead of capitulating to the threat of the Baldwin government’s resignation if the King persisted in his plan to marry Mrs. Simpson, the King could have engaged such supporters as Lloyd George and Winston Churchill to serve as advocates and possible leaders of a coalition government willing to acquiesce in the King’s proposed marriage to Mrs. Simpson. Ultimately, the thesis of this paper is that there was no legal impediment to a marriage between King Edward VIII and Wallis Simpson; rather the issue raised by the King’s desire to marry Mrs. Simpson was political, and the abdication could have been avoided if political options had been pursued.