The FMS is not "Client's operational equipment", it is part of the basic aircraft and thus must be serviceable unless allowed to be U/S in the MMEL/MEL. Which it is, but with the caveat "provided procedures do not require their use". And for the GPS "as required" (by operational regulations).
So taking the bureaucratic view, if the FMS forms part of the SOPs and procedures in the OM Part B and it does not make provision for when the FMS is inoperative, you can't depart. If the Operational Regulations require you to have GPS, you can't depart.
From a common sense point of view, it depends on the intended flight. Presuming the above criteria were satisfied I would look at the flight, the availability of other navaids / visual nav, the need to navigate accurately (traffic density, risk of "missing" the offshore installation, terrain etc), the weather, the tightness of fuel planning and make a judgement call. If it was "out in the bay" 20 miles offshore, then probably yes. If it was 280 miles out to sea with no navaids after 80 miles, then no.
In the case of Bristow, the FMS/GPS forms a basic part of operating offshore as far as the Operations Manual goes, so the answer would always be No.