Yes, as hosemary has explained above, you can sign the message at any time ad long as you have the addressés private key.

In this specific case, most people will accept a signed message as a proof that you are the one who initiated the transaction. But this is not always true. Signing a message only means that you know the addressés private key but it doesn’t ... that you are the one who initiated the transaction (it could be someone else who also knows the private key).

You can sign message from any address you own at any time and it has nothing to do with the time you made your transaction.
And It may worth mentioning that you sign the message locally on your own device without any need to the internet and without any information about the transaction history of the address.