They show up as a gratuitous, white square which turns creating damage points for your fighter into a game of pin the tail on the donkey.
Unless, of course, you create a separate _damaged.dds (square) texture which does show up when selecting damage in the graphic selection buttons.
Did this with one of my fighters (see below):
To me, it looks like the editor is taking the information in the hull text file too literally and is actually looking for a fighter_damaged.dds texture
while the game happily extrapolates from the _sprite.dds.
Any thoughts? Conspiracy theories? 
I think the only purpose of a damage.dds file in case of fighters is only to see that dmg sprite in the editor. The game will always pick up (as far as i know) the damaged sprite located in the myship_sprite.dds file. I think.
Yes, that is true. I’m just curious as to why that is.
This is a hangover from the way the game was developed. Originally, the fighters had damage sprites like every other ship. Then, when the game was being optimised, they were shrunk down to smaller size, and grouped in with the other fighters so there were less texture-swaps when big fighter-heavy battles got drawn.
By then, the damage textures had already been done 
When I add new ships, I manually do a damage sprite like you have done, then I shrink them down and bunch then together once everything else is done.