People do hunt beaches all around Lake Michigan. Minelab recently held a major event at the Indiana Dunes State Park. "Treasure hunting" on wrecks in the Great Lakes is prohibited.
Get there at first light, you will see plenty of others md'ing the beaches in the early hours on some days. The biggest takers of loot and lost items are as Jason mentioned, the beach pickers. Those park district cleaning machines scoop large volumes of stuff up from the sand and it disappears forever with the guys driving them. I really doubt they have a lost and found bin at their dump site.
Then again I really doubt there would be much in the lost and found bin if they did have one...
At least us MD'ers have returned many items we have recovered from those beaches. Everything from jewelry to cell phones, wallets and purses. But I do tend to keep all the pocket change I find so I can get some snacks while there, and pay for parking when necessary.