Yes it does.The coin doesn't exist without adding the correct hash to the blockchain.
The hash IS the Coin.The hash may be correct but it won't become a coin unless you are first to record the hash.
You are speaking of a transaction again. Math errors: failure to declare boundary. Failure to declare randX.So you can get all the hash results you want. None of them will be Coins until you are connected to the internet. The odds of getting a correct hash when not connected and then being first when you do connect later are so low they might as well be zero.
Argument from randU fallacy.
