If it is, are there any known cases of this form of suicide in the Harry Potter universe?
I think it could probably be used to commit suicide.
The only example anywhere in the canon comes from the video game of Deathly Hallows: Part 1. There’s a YouTube walkthrough which shows the Tale of the Three Brothers, and Cadmus Peverell appears to commit suicide using the Killing Curse. (It isn’t explicitly stated, but he turns his wand on himself, and dies with a flash of green light. It seems to fit.)
However, the games aren’t necessarily canon. In the movie animation, he hangs himself, and the method of suicide is unspecified in the original tale:
The second brother, driven mad with hopeless longing, killed himself so as truly to join her.
And so Death took the second brother for his own.
I don’t know of a better example in the canon than this.
Could it work? I suppose you might fall afoul of the rule “a wand cannot kill its master” that trips up Voldemort at the end of Deathly Hallows, but I don’t know if that still applies when it’s you doing the casting. I think if somebody is competent in the spell and feels strongly enough that they want to die, then they could probably commit suicide this way (and if not with their own wand, certainly with somebody else’s).