That would conclusively prove it.
I don't think it would, as I've discussed in other threads previously. It would prove ownership of the private keys, but it would not prove identity. It is an important and necessary first step towards proving identity, and without it anyone claiming to be Satoshi can be ignored, but on its own it is not enough.
That account is locked by Theymos, this kinda raises the interesting question though of whether there would be something to persuade him to unlock it (for the real satoshi - or a good masquerader - if they return).
theymos previously said this about it:
His account is locked, so no. If he wants to claim his account, he'll have to contact me with a PGP signature.
That was over 8 years ago, though. Perhaps his opinion has changed and he would require more proof than a PGP signature.
Signed message also works, but CSW and co found some loopholes which makes their signed message appear legitimate.
There are no loopholes. They performed parlor tricks, including on some people who really should have known better. Nothing CSW has presented has ever come close to being considered legitimate.