That is not the standard procedure no. After step 4 the wallet will believe the tx has been broadcast and will not immediately attempt to rebroadcast it.
The normal procedure is to use an online wallet to construct a raw transaction. Copy raw transaction to offline wallet. Have offline wallet sign the raw transaction. Copy signed raw transaction to online wallet. Have online wallet broadcast the signed transaction.
I don't understand what you mean by raw transaction, or I must have missed that on Bitcoin Core.
I think you'll have spell that one out for me or walk me through it.