[bluepizza]

I understand OP's question to be more practical than honour and family - literally as "Would the Japanese recognise a marriage performed in England?".

Civil registration started in England only in 1837. Modern koseki system in Japan started in 1872, but different systems of civil registration existed way before that, including one created under the shogunate (though many years after Adams's passing).

And indeed, they couldn't possibly careless about his married status regarding him marrying a Japanese woman. His declaration of death was so that he would be free to serve the shogunate freely, without the obligation of return to his family in England.

Neither bureaucracy nor family honour.