The problem is the PCM could have been damaged by the short in the wiring harness. The wiring may be repaired but the replacement PCM could be bad now.
Either way, there's no way that applying power (through the test light bulb) could have made the injector click unless there was a short to ground in the circuit elsewhere. Something has the circuit shorted to ground at some point. You've cut the original driver wire at the PCM and injector both?
I'm surprised they warrantied the PCM knowing there was a wiring issue when it was installed.
If it's running ok and not setting the injector code any more then go ahead and drive it. It might take 10-15 minutes of driving at highway speeds to get everything dried out and the smoke to clear up.
If you had low compression then you'd notice number 4 missing. If it's running smooth you should be fine.
It's still going to be wet from all the fuel that was poured on it. If the smoke doesn't clear up after a test drive then we've got more problems, but at this point I'm not worried about it. If it was fine before and the injector code is no longer setting then I'm confident it will clear up when the engine and exhaust are held up to operating temperature for a while.
The smoke isn't going to go away for hours if you just allow it to idle in the garage. You have to drive it to get everything to operating temperature and keep it there long enough for everything to burn off.