Can I generate payment adresses while offline? So I'm using the original bitcoin client.
What if on a computer without internet (A) I generate a bitcoin address and
then use this address to receive a payment (by using an other computer with internet (B))

Once I transfer my wallet.dat to computer B and let it sync, will I still get the payment ?

I'm asking because I'm doing stuff from work and the bitcoin-qt can't synchronize from over there.

Do I need to be online in order to generate a ready to use payment address?
No, you don't need to be online when generating a new receiving address, as this is done locally by your bitcoin-core. You also don't need to be online to receive funds to these addresses, as long as you protect your wallet and keep your system free from malicious software you are the owner of these addresses and you will be able to check their balance as soon as you get online and let your wallet synchronize with the network.