That may sound like a silly question, but if I have created my keys using a passphrase in “brain wallet” at bitaddress.org, why do I need to record the private key, if I can recreate it at any time by using my downloaded version of bitaddress.org?
To be sure that I can do that safely, I need to know whether the algorithm to generate a private key from a passphrase with a downloaded copy of bitaddress.org is deterministic.
"Is the algorithm to generate a private key from a passphrase with bitaddress.org deterministic?"
, as it seems that is what you wanted to ask. I'd say that your approach is viable, if a) you make sure that a copy of bitaddress.org remains available to you, and b) the algorithm used by bitaddress.org is in fact deterministic, which I don't know for sure.