I haven't tried either of those methods but when I most recently completed Gold Digger, it wasn't completed when the dead spouse was a ghost but after Grim had left the premises, so I'm doubtful.
My two pieces of advice:
1. Make sure you meet the spouse at their home before you marry them or move them in. That's how it registers that they're rich.
2. The Gold Digger has to actually see the death! My harrowing story about this is when my rich spouse died on the other end of Bridgeport and I had to make sure his wife was taking the fastest car we had (Motive Mobiles are so slow). There really wasn't much time to spare. I probably wouldn't separate the two again.