Appeal after dead ball, runner returns

[orioles35]

R2, B1 hits fly to right, which is caught and R2 obviously leaves early. RF airmails the throw over the 3Bs head, over the fence and into DBT, R2 scores.

Obviously, the ball is now dead and nothing can happen. R2 realizes they are going to appeal his leaving early once the ball is in play and after crossing home (but before getting to the dugout), he proceeds to return to 2B.

While there's a dead ball, can the runner do this, even if he retouched home and 3rd? The defense hasn't had a chance to appeal because the ball is dead. If R2 shouldn't be allowed to return to 2nd during a dead ball, how can this be prevented?