If I send Bitcoins to an address which's offline what will happen?
There are no offline addresses.
As per my understanding, sending Bitcoins to an offline or non-existing address
There are no valid non-existing address. You can either make a valid transaction and send the coins because the address is possible or you cant make a transaction at all.
There are certainly addresses that no belonging private key exists for yet. If you send coins to such an address they will be lost forever.
will not eat up my balance cause the receiving address needs to be broadcasted by the receiver and that broadcast needs to be recorded in the block chain, since the receiver is offline, this broadcast wont happen.
No, you just make a valid transaction (you can spend the former input as a new output = you have the private key to spend the funds) for a possible reiceiving address. You then broadcast that TX. Validity is checked, but that does not include a check whether the private key for the receiving address has yet been created. A check like that is not possible anyway. After a while the TX gets included in the next block and the coins are no longer yours.
It is possible that the coins now belong to noone.
So if I rescan my wallet, I should get my Bitcoins back.
No, they are gone.
Edited to to avoid confusion