No
If neither ship chooses boarding, no grappled and no boarding.
If both choose boarding then ships grappled and boarding takes place
If one side prepares a boarding party and the other does not you draw to see if the boarding takes place

Once boarding has been decided and one side chose prepare and the other ship does not then the ship that chose not to have a boarding party takes another chit, so could possibly lose another crew. That is the advantage of choosing a boarding party or disadvantage of not choosing the boarding party.

Does that explain it better ?