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).
Thanks for your answer! And can I also receive coins immediately ( well, with the standard time you have to wait ) on blockchain.org and uninstall the program? – Ahmed – 2014-02-17T20:30:09.327
What coins are in your account depend on the blockchain, not your software, so you can start receiving bitcoins immediately. You will, however, not SEE the bitcoins in your desktop software until you are sufficiently up-to-date. You can go to blockchain.info and type in your public key (or anyone else's) and see your newly arrived coins immediately, since they are up-to-date. – AMADANON Inc. – 2014-02-17T20:40:28.967
@AMADANONInc. Thank you, very clear. But doesn't that mean my newly made public keys aren't in the bitcoin chain yet as well? – Ahmed – 2014-02-17T20:46:07.597
Newly generated keys are never in the blockchain, until they receive money. Receiving money puts them in the blockchain. – AMADANON Inc. – 2014-02-17T20:47:49.663
@AMADANONInc. Good explanation :D Too bad I can't vote up here – Ahmed – 2014-02-17T20:49:22.220