DME relay schematic via Clarks Garage:
The DME control unit must be turned on by the DME relay, and the control unit powers many items including the idle stabilizer unit so in that sense, you would be correct. But it does not directly power the idle stabilizer, unless I am really misunderstanding something, in which case I do apologize.
IF the DME relay is faulty, you can jumper 30 to 87 and 30 to 87b and the car will be driveable, as long as you take care to remove the jumpers each time you turn the car off - otherwise the fuel pump will run until the battery is depleted.
Ruling out the idle stabilizer should be pretty simple: accelerator to the floor on start. If it fires up, could be the idle stabilizer (not necessarily though). If it still fails to start, it is pretty definitively not idle stabilizer.