From what I can tell with experience- most bans come from players hitting that report button OR simple negligence on the botter's part. "Negligence" being bad ips, script errors, botting during jagex hours, botting with multiple accounts on the same ip, botting too much, using free scripts, having bad account names.
If it seems like it could help you to not be banned its almost like 80% certain that it will HELP. However the %chance margin may not be that high & it may not be worth it to go through the extra precaution to ensure your accounts don't get banned. I'll give you a tip though, botted f2p accounts are very likely to be banned. Even if you're playing legitly at willows on 3 different accounts & 3 different worlds but on the same ip-you might get banned. People toss around reports like its a hobby, bots plague the game. All the "security system" knows is that some player thinks you're a bot. It probably checks to see what you're doing.. ok this guy is on 3 different accounts at once-instant ban.