I think that might be a lot of work for a tiny mount of gold, but the possibility is there. I knew a guy from New York who would clean the cracks out of the sidewalk in the Jewelry district. He would find tiny gemstones, even diamonds, and a lot of gold or silver dust. Over time, it all adds up.
For many years, I collected electronic parts from old printers, PCs, hard drives, cell phones, etc. and would strip the gold from them. It is a lot of work, but there is quite a bit there. Not enough to get rich, or even make it worthwhile (so I learned).
Most people don't know that hard drive disks are coated with an extremely thin layer of platinum. I learned about all of this while installing a security system at a local recycling plant. They had two large vats filled with acid that would dissolve the gold from all of these components.
When I came to South Dakota and began studying the mining history of the area, I learned that most abandoned gold mines still contain gold.
During World War II, many gold mines were closed by the government because they needed miners to work on mining metals to support the war effort, like copper and iron. Then many of these young miners were drafted into military service. Some never came home, others were too old or disabled to work in mines.
The price of gold was so low and the cost of mining was too high, so many mines just remained closed. Lately, with the price of gold rising, mining companies are exploring and reopening the old mines. The price of gold is high enough that the efforts can now be profitable.
I am not a hard rock miner, so I stay away from the old mines. They are too dangerous with rotting support beams and many used toxic chemicals like cyanide, mercury, or arsenic. Instead, I study geology maps and look for patterns where the biggest mines were located. That tells me where the gold veins were in the rock. I then move downstream and sample the soils to see if any of the gold has eroded out.