If that detour is and remains open it looks like a reasonable alternative for touring riders.  It would allow great views of the Tetons, but none of the geothermal stuff In Yellowstone, which obviously are a highlight of the TA for many.  It will be sad if many will miss that possibly for years to come.

Per Flood Recovery and Operations - Yellowstone National Park (U.S. National Park Service) (nps.gov) the NPS will reopen the southern part of the Park on June 22.  They'll use an "Alternating License Number" system to limit the number of vehicles entering the park for day use.  There's no specific mention of bicycles in their plan.

If you are fortunate enough to have proof of a reservation at any of the to-be-reopened campgrounds or lodges, you're good to go, regardless of license tag number.

Ja.
I know the park is reopening on Wed. and I am expecting to get to West Yellowstone around noon on Wed. But I'm not sure if I will ride thru Yellowstone this year. Still not sure if they will let bike in or if hiker/biker campsites will be available. But, most importantly, I'm guessing it will be a total zoo. In the past I've been able to ride early and late, but I fear those windows will be busy, too.

John, I'll be reading your posts with more than academic interest.  Good luck to you.