as above

I would have thought so. French uses a remnant of the dative case 3rd person singular pronoun in 'lui envoyer une lettre" (send him/her a letter.) It would make sense if that came from Latin. However, it doesn't seem to. I can't find anything in my Latin dictionary under 'mitto' besides constructions with 'ad + pronoun/noun/name." Maybe someone else knows more?

It seems it is just not how Romans talked about sending letters. They used the construction ‘litteras/epistulam ad [name/pronoun in accusative] mittere’.

Romans thought of all the individual letters that go into writing what, in English, we call ‘a letter.’ They might ask us, “Why do you call it ‘a letter’ when you use so many letters to make it?” :) They also used the singular ‘epistula’.

The singular "litteram" would mean a single letter of the alphabet, rather than a missive.