I've got many battle.nets - but two 'main battle.nets' which always have my 'active' accounts in them.
When an account gets banned, i move it to my ' cata+mop graveyard' battle.net.
So far, it has 5 banned accounts and I tell you what - IF they ever open them back up, It's going to have some serious achievements/mounts/pets/collectables.
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To answer the OP directly, if you get flagged and banned on one account, other accounts on that battle.net are NOT automatically banned. However, there is a logical increase that they'll be checking for injection/suspicious behavior on those other accounts too.
People here (as they always have on pirox, glider, etc) will spout all sorts of garbage about IPs,Hardware IDs, etc. When there has never been any solid evidence to support it.