It depends on what the configurations are approved and the manner of their approval.
If the modification that installed the EMS fit also covered a configuration where the fixed fittings only installed then it is entirely possible that the Part 1 FMS may include reference to this configuration. If this is the case then the FMS is required.
If however the fixed fittings are installed and approved under a different modification from the main EMS fit then it is highly likely that there is no Part 1 FMS required for these.
To be fair you really need to talk to the STC or major change approval holder for your specific installation to find out. In our company we have always tried to separate the two issues for just this reason and to keep flexibility of the aircraft. This really helps in organisations where there may be a backup aircraft that may perform other tasks when not required