I mean, the coroner must at least have known that he had a chemistry lab, working with dangerous chemicals, in the house. That's way more unusual than gaying it up.
Do you think a dead man with breasts would have gone unnoticed by the coroner? Do you think he might have wondered why Turing had breasts?
It's quite reasonable to think that the coroner would have known that he was homosexual, and it is quite reasonable to think that would have been viewed as a flaw, since, you know, the whole state-sanctioned "choice" between prison and chemical castration thing.
That seems quite plausible. The coroner would be aware of his criminal conviction as a matter of course, but might have relatively little information about his profession.