That's a no, it's bound to battle.net account, not WoW account.
I have the same mounts on WoW 2,3,4,5 etc. as i do on WoW1. At least that's what they told me on customer support.
They also said that originally it was bound to both character and battle.net account, but this was used for exploitive behavior and they were forced to remove the bound to character part..
I guess too many people had a friend / paid someone to move their character to their account, logged on, benefit from all achievements and mounts, moved the character back..
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