Almost on a daily basis someone will ask the field crew if they've found any gold yet. Over 99% of the time the answer is no. The reason for this is simple. Most of the objects left behind by the colonists were intentionally discarded, but that was not always the case. Sometimes the archaeologists discover more valuable objects.
Although incredibly rare, the archaeologists occasionally come across gold artifacts at the James Fort site. We have catalogued nearly 2 million artifacts, but only half a dozen gold artifacts have been found where they were left in the early fort years. Three of these gold objects were found in the rubbish layers of a cellar that once was used as a blacksmith shop and bakery. After the cellar was abandoned, it was filled in with these trash layers where the three objects were found. Among the half dozen gold objects found during the project's first twenty years are small chain links, a short strand of gold wire, and a gold puzzle ring.
So the answer to the question is yes, we do find gold, but it is extremely rare.