It depends on the braille table. There's an Esperanto braille table you can use if you want to be absolutely sure they do. NVDA has support for it.

Some screen readers do not announce them by default, though a person using a screen reader to read Esperanto would probably have found a good way of reading Esperanto.

NVDA supports Esperanto grade 1. About announcing the diacritics, if you use ESpeak for Esperanto, it will announce them and you can read Esperanto with it too. But if you use other voices, you'll most likely have to add them manually. As far as I remember there are 6 letters with diacritic in Esperanto, each having a lowercase and uppercase version. You have to add them one by one.

bonŝancon