While it's probably safe to say that the UP shoreline area near Lk Superior probably doesn't get the thick flights, it would certainly be possible that there are some flight birds. Woodcock are tougher and stronger birds than their size would suggest. When I was involved with the banding program a GPS fitted woodcock flew from southwest Michigan to near Green Bay non-stop in one night, into a headwind. The GPS trackers in the last few years have greatly expanded what biologists thought woodcock were capable of.
The excerpt below is from Project Upland. I don't remember if the 500 mile flight mentioned is the one I described or not but a really fast line distance north to south across Lk Superior is about 170 miles.
While a single woodcock has been recorded flying almost 500 miles in a single night, the American Woodcock journey requires “stopover” habitat.