As a board member of the formerly 3rd largest off road event in Moab....
No, you can not close public lands. Thankfully, otherwise the eco-nuts would certainly use this against trail use.
You can TEMPORARILY limit or control traffic on a trail, IF, you are using the trail under a BLM permit or other authorization that more specifically required INSURANCE as a rider and contingent to your approval to use the trail.
Now with that said, during EJS and I think you are silly to be there during EJS and NOT participate in the event (it makes much more sense to go to Moab to actually wheel not in a traffic jam)..... I have seen closures of some areas and trails. More specifically such activities like Lions Back have been closed by the enforcement of the Moab PD/Sheriff office because of too many stoopid people. Same goes for Potato Salad Hill.
EJS is a great event. But if you are going to Moab to wheel, I would go on a less busy weekend. If you are going to Moab for EJS, have a great time, but join in the event and expect some "issues" with being in a crowded location with more people than the town can reasonably handle. I am in no way dissing on EJS its like going to Woodstock for the music and none of the rest and possibly bigger part of the event.