Will the accented letters in Esperanto show up when using a Braille display if the Braille display doesn’t specifically support the Esperanto language and if so how would they show up?
Most likely, this would depend on the Braille tables available in the Braille display's "driver" or screen reader. For example, the open-source Braille translator and formatter Liblouis has Braille tables for many languages, including Esperanto. At the bottom of the Braille table for Esperanto I find the following codes for a number of accented letters:
uplow Ĉĉ 146 LATIN LETTER C WITH CIRCUMFLEX uplow Ĝĝ 12456 LATIN LETTER G WITH CIRCUMFLEX uplow Ĥĥ 1256 LATIN LETTER H WITH CIRCUMFLEX uplow Ĵĵ 2456 LATIN LETTER J WITH CIRCUMFLEX uplow Ŝŝ 2346 LATIN LETTER S WITH CIRCUMFLEX uplow Ŭŭ 346 LATIN LETTER U WITH BREVE
Liblouis is used in the open-source screen readers NVDA (for Windows) and Orca (for the Gnome desktop on Linux).