Suppose one has an unusual or foreign name, or a name which traditionally belongs to the other gender. Is it inappropriate to add one's title (i.e. Mr/Ms/Mrs) to the signature of a letter/email so as to identify the author's gender?
It is not. You shouldn't. Don't. It would be silly and impolite. People would throw garbage at you.
You could use a trick or two, though. You could insert a nickname between the Christian name and surname. As in:
Laballa "Gentlemanly Jack" Barocca, Esq.
Affectionately Yours, Drapezhnik "Bubbly Jill" Femistodinzs