To answer your question -
A) Yes, this transaction will flow through to QuickBooks.
B) In short - you only have the inital sync from Method to QB if your transaction history is set to 'none'. S ince you have set the transaction history to 'None', the newly created transaction will be removed from Method on the next Full Sync. While the transaction is still in Method though, changes to the transaction in Method will not flow to QB, and changes to transaction in QB will not flow to Method.