Golf courses use a similar technique when moving holes and have never had any issues.
Yes they do have issues buddy.
They use a special circle cutter, then they take the removed sod and put it in the old hole. They pack it with sand and water it heavily. After all that, sometimes they still suffer and discolour.
Coins and artefacts are different sizes and sit at different depths. The point where the signals drops can vary, so in my honest opinion and experience, cutting plugs the size of golf holes can lead to damaged finds and damaged grass. I learnt that the hard way.