"...the Volvo guy says it cooks the ECU."

I'd look for another Volvo guy. All you are doing is putting +12 where the Fuel relay does, when all is OK.

Your circuit sounds relatively safe—except in an accident where you might not be able to switch the ignition off.

Here is the start sequence:

1) During starter cranking, the Crank Position Sensor (CPS) sends timing pulses to Ignition Control Unit (ICU).

2-a) The ICU propagates these timing pulses to the Power Stage (aka Ignition Amplifier) to initiate spark at the coil.

2-b) The ICU also propagates these pulses to the FI ECU, to allow FI operation
(no ICU pulses means no FI operation).

3-a) The "System" relay (in with Fuel relay, and previously energized at Key On) powers the AMM, IAC, ECU, Injectors, and Fuel relay coil + side.

3-b) When ICU pulses are received, the ECU "energizes" the Fuel relay (completes the relay coil ground side) to run the fuel pumps.

When all these things work, the engine runs until the Ignition is switched off, which in turn shuts down the FI system.

--
Bruce Young, '93 940-NA (current), 240s (one V8), 140s, 122s, since '63.