Is it possible to shoot an electronic flash with an Argus C3? Well, yes, it is possible. However, you will have to do several things to enable this.
1. For true X-sync, you'll need to alter the cameras flash timing. The camera was originally setup to fire that bulb flash, so right now the camera is timed to fire the flash slightly before the shutter is fully open. This allows for the flashbulb to reach the peak output when the camera's shutter is completely open. However, for an electronic flash, you don't want this delay. So, you'll need to open the camera up (remove the leatherette on the front of the camera, remove the shutter cocking knob, and remove the four screws holding the faceplate to the camera body). Inside, you'll see the shutter mechanics. If you search the internet for Rick Olsens camera notes, he has a great description and diagram of the C3 shutter.
2. You'll need to find one of the uncommon PC-flash adapters for the Argus C3. If you can't find this, it is possible to rig something up using the original flash. Again, searching the internet should come up with some ideas.
3. You'll need to test your setup to be sure you have the flash timing correct. A quick test involves mounting the flash, opening the camera back, setting the aperture to the widest setting, and pressing the shutter release. You should see a bright light through the lens if the flash timing is correct. Still, you should run a roll of film through the camera to be absolutely sure.
I know this answer covers everything fairly briefly, but the information is out there if you look carefully. I'm just answering your question from memory and based on experience with using/repairing the C3. If you still have trouble, feel free to say so. I'd be more than happy to locate the specific information you need.