No.
Under regulation 5(1) a Safe Manning Document must always be in force and on board, and the manning of the ship must be maintained at all times to at least the levels specified in it. Under Regulation 5(2) the master must ensure that the ship does not proceed to sea unless there is on board a valid SMD and the manning of the ship complies with it. There are no provisions permitting sailing short-handed with respect to the SMD.