The answer to your question will very much depend on implementation details, but you might not be versed enough in cryptographic protocol development to know exactly what to ask, so I'll take a stab at answering this and hopefully my attempt will help you refine the question as needed.
- How are the blocks/streams after decryption synchronized at the receiver to form one long meaningful message?
Sychronization is often done before decryption. Wrap the ciphertext with a protocol header, throw a sequence number into the protocol header, authenticate the entire thing (header and ciphertext). The receiver, after checking authentication, can order the ciphertexts using the sequence number and then decrypt.
- Am I right by saying that stream cipher will incur a LOT more overhead while synchronizing?
If you look at my description of how synchronization could be done, you'll notice that it is symmetric-key cipher agnostic. Thus the synchronization will be the same whether we are using a block cipher or a stream cipher.