Looking at this with an open perspective.
Does botters pay for keys and gametime? Yes
Did Blizzard make this game to earn money? Yes
Does Blizzard waste resources to monitor you old banned B.net? Hell No
With that said, they aren't monitoring your accounts, but if you ever give them a reason to invetigate your account, and you happen to have previous banned accounts on the same B.Net, it is likely to sway the GM's decision.