An independent treatment of wheelies in Gray Costanzo and Pleshas  Dynamics textbook begins with the full NewtonEuler equations and so necessarily includes the vehicle moment of inertia They then calculate the maximum possible acceleration of the combined bike and rider rigid body such that the front wheel does not lift off the ground in other words the acceleration that causes vertical load on the front wheel to decreased to zero With this constraint the angular acceleration is also zero and the only term which includes moment of inertia is eliminated Thus their analysis seems to say exactly that wheelies cannot begin until the front wheels bear no vertical load and whether a vehicle when treated as a rigid body experiences a wheelie or not is independent of its moment of inertia