Speaking as a Minnesota State Park Ranger, I'll confirm that in our state parks and forest recreation areas,we will never turn a cyclist away. We will find a space for you, even if it's next to the dumpster! I have put cyclists in empty group camps,(one little tent in a 5 acre camp site.) picnic areas and on the edge of parking lots in the past. I have also had cyclists (two, to be precise) stiff us on the camping fees, one for six nights worth. Just to make me feel better, I had one guy biking through who only had one and a half nights fee on him, and I let him stay the second night. Danged if three days later we didn't get a check from him for the remainder and a bundle of firewood!
I would agree that you should at least check in with local police, rangers, etc. for your own safety, if nothing else. I remember when I was with the NPS years ago, the Morning Report (transmitted to all NPS units each Monday - Friday) recounted the search for two cyclists who camped in a area closed for safety reasons, and were washed away by a flash flood. They were found dead, downstream, two days later, still tangled up in their tent and sleeping bags. If they had stopped and asked, they would have been directed to a safe area.
Hans Erdman, WEMT
Backcountry Trail Patrol-MNwww.trailpatrol.org