Yep, last version of Amethyst re-broadcasts on quotes, boosts, replies and mentions to posts.
Discussion
Damus does it when replying but doing it on quoted reposts is a good idea too
nostr:note1sqnfunexsyn89ggdxgdky5j50ezh6s9mtjncy9yfq9683c8x82jqke0vca
Vitor, The Master of NIPs, says that the latest version of Amethyst rebroadcasts the original note to all of your relays whenever you boost, quote, or reply to the original note.