If you try to manually crawl the post with Internet Archive's "liveweb" project (which inserts stuff into Wayback Machine for live lookups) you'll get:
"Page cannot be crawled or displayed due to robots.txt."
So no, the Internet Archive will most likely not archive public Facebook posts - because of Facebooks robots.txt. The IA respects and honours the domains robots.txt.
I've taken a snapshot of the post with my own script which will put it into a IA Wayback Machine friendly format (WARC).
"Page cannot be crawled or displayed due to robots.txt."
So no, the Internet Archive will most likely not archive public Facebook posts - because of Facebooks robots.txt. The IA respects and honours the domains robots.txt.
I've taken a snapshot of the post with my own script which will put it into a IA Wayback Machine friendly format (WARC).