Private keys can (and should!) be backed up as soon as they are created. You do not have to wait for the blockchain to sync, and in fact new accounts don't exist on the blockchain until they get some bitcoin in them - receiving your first bitcoin to your address is what adds them to the blockchain.
Since the balances of the accounts are stored in the blockchain, you also don't need to back up as your balance changes; the balance the blockchain credits to your private key will change, but your key itself never will (unless you create new accounts).
If your desktop client is not yet up-to-date, you will not SEE your bitcoin; once your client passes the block which shows your arriving bitcoin, it will magically update; spent coins, similarly, will only show as you download the relevant block.
You can always see your (or anyone's) up-to-date balance by typing (copy/paste) the account number into blockchain.info's search, since they have the entire blockchain (and keep track of the unconfirmed transactions that are not yet in the blockchain).