As I understand it, the boat has an existing cord with a male end -- a shore power cord, or similar -- which feeds the AC outlets throughout the boat. You'd like to plug that cord into an inverter in order to have mains voltage supplied by the battery and inverter. The question is whether the receptacle on the inverter should be the ordinary type or the GFCI type. Did I get that right?
In my opinion GFCI exists to protect personnel, not wiring. Because the boat system already provides GFCI protection for all outlets I suggest that having GFCI protection at the source too is unnecessary. (Assuming that the boat's existing GFCI work properly with your inverter, as noted in Ed Beal's answer.)
I'd even go so far as to say GFCI in the inverter would be undesirable: as noted, the inverter will be in an inconspicuous location. If a GFCI in that spot were to trip the consequences could be inconvenient (or worse?). It could be that the inverter's GFCI might be more sensitive than the others in the boat and would trip first. A person unfamiliar with this boat's system might spend a lot of time troubleshooting to discover the multi-level GFCI protection.