Yes, the FMM920 will function well even without the OBD, you only need the OBD if you want to add an OBDII dongle to your FMM920 device.
For basic track and trace, you only need the ignition wire and the power.
Immobilizer for FMM920 is possible using BEACON as an authorization device because FMM920 does not support 1wire, to do this you only need to connect the ignition cable DIN1 to the ignition wire of the vehicle and install the relay connected to the DOUT of the vehicle, make sure that you have set the immobilizer functionality to LOW or HIGH to enable the feature.
There is also another method where you need to send GRPS or SMS command to activate and deactivate the DOUT on this option no need to enable the immobilizer functionality from the device, just install the relay and connect it to the DOUT.
Reference: FMB920 Features settings - Wiki Knowledge Base | Teltonika GPS (teltonika-gps.com)