Yes, but the ecu may still have damage that won't allow it to ground the coil in the relay. I would try checking/replacing the relay first (junk yard part - the relay is NOT usually a failure source).

The most common source of failure in efi systems is the wiring harness connections and power supply paths (connectors, fusible links, fuses, circuit breakers). If I had the wiring harness diagram for the efi, I could give you exact spots to check.

Without the diagram, these are in part just educated guesses based on prior mitsu models with similar engines. The efi relay probably supplies power to the ignition and at least part of the ecu as well as the fuel pump. They used to be called dual relays because there is actually two relays in the steel box. The efi system needs ign switched 12v+, unswitched 12v+, and ground, plus the various sensor inputs, power to the sensors, sensor grounds, and actuator outputs (injectors, fidle valves, idle stepper motors, ignition timing control, tranny controls, throttle by wire, etc.) and the dual relay coil ground that controls that fuel pump relay. I would try to identify the individual relay connectors and check for constant 12v, ign on 12v, and ign start 12v, apply battery power to the relays' coil circuits and check power path continuity to the ecu (and ignition) and fuel pump in both ign on and ign start states. In the process, unconnect and reconnect all the ecu and relay connectors, spraying in between with electrical contact cleaner from RadioShack or equal. The efi main common ground should be somewhere on the body metal near the efi relay and ecu, probably on the passenger footwell sidewall, and should have several black wires all grounded there. The factory shop manual should show the location of all the common ground points. While you have it opened up enough to look at this stuff, take the ecu loose (a cover, a couple of connectors you want to clean up anyway, and probably 2-3 10mm bolts and remove the ecu case cover to expose the bare 'lectrons and the ecu printed circuit board and sniff for a dead fish smell which is diagnostic for capacitor leakage.

Mitsu factory manuals have a detailed section on reading circuit diagrams (how the wires are connected and to what with what kind of connectors and with what weight wires) and harness diagrams (how all the wires and connectors are physically routed in the truck), including meaning of all the symbols and wiring codes. It takes some study, but once you get the hang of it, you can trace the wiring paths for each device and find the wire location in connectors and harnesses, the color code of the wire and it's identifying stripe(s), the heaviness/gauge of the wire, and what else the wire is connected to, and where the whole circuit grounds.

I trace circuits from power source to final ground point on the diagram, like following the path of water in a pipe system. The battery is the water souce. The ground is the final drain for all the water the devices did not use. Fuses are safety valves. Switches are valves. Resistors are pressure limiters. Flow quantity is current so lots of current needs fat pipes (wires). Voltage is pressure in the pipes.