I think that is the case. I have not had any problems when rejoining just a few days after deleting my previous account.
You can join again all right, but when you 'delete' your account it is deactivated rather than deleted which, according to AW, takes one month. An alias shows up against your profile only on an SP's screen - just shows up as red. Sometimes the SP can click on it to see the different aliases. So if you have had a shite one and start again you had better play by the rules or check, I'd say.