Can I still buy Minecraft with a username I never registered but gave to Mojang and get a cape?

I have a Minecraft username that I made back in 2011 that was never made into an account, but is tied to the capes they attached to the usernames at Minecon 2011. They required a username, so I gave them one, but I did not purchase the game with said username. Can I still purchase the game with this account and get the cape?

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