To see a thestral, you have to have seen death and processed it. (Hence why Harry could not see thestrals at the end of Goblet of Fire, as established in answers to this question.)
Do ghosts count, in regards to their own death?
Two problems present themselves to me: first, if you're the one dying, are you "seeing" death? With Avada Kedavra, Harry Potter is a universe where death happens in an instant. It's not a process. Can you "see"/"experience" yourself expiring when that very perception is [initially] dependent on being alive?
Second, Nearly-Headless Nick makes clear at the end of OotP that ghosts are what they are because they feared death. They have not gone "beyond the veil", so to speak, and the theme of accepting death and moving beyond this world is explored in some depth in books 5, 6 and 7. Does the "death" of one who becomes a ghost count? By virtue of having made the choice to become a ghost, do they lack a crucial element of this "sink[ing] in" that JK Rowling mentions in the linked answer?
I'm curious if there's a Word of God on this, or some throwaway line in the books where a ghost interacts with a Thestral which I've missed.