It may very well be reported as plagiarism, by a user or a bot, but I would think you would be very unlikely to be banned for it. If it is quite obviously supposed to be a quote, and you have just messed up the BB code, I'm sure the moderators would realize that and not issue a ban. I'm sure I remember this exact scenario being discussed in a meta thread a while ago.
I think you are right. After receiving reports from forum members, mods will do their tasks, and at the end, admins or global mods might recheck reported cases (that already checked and confirmed by mods) before doing perma-bans.
We likely have tripple-checking procedure: Bots/ Forum members > Mods > Global Mods or Admins.
What's next after reports of plagiarsims?Posts are reported to moderators who check out the report. If the poster needs to be banned, the moderator sends a ban report up to a global mod or admin. The global mod or admin handles all of the ban reports they get at around the same time. Either the admins or global mods don't need to check every account because they trust the moderators to have already done so, or they check quickly because every such report contains references and links to the plagiarism post and to the source text so checking takes little time.