IMO, a player entering the game for an injured player should be granted the same rights that the injured player had to complete his running responsibilities. In either case of the ball entering the dugout or the official declaring time due to injury, I'd grant the substitute the right to correct the error within the rules.
IMO, calling of "time" causes the ball to become dead.
If continuing play was occurring---including an appeal by the defense for the miss of 2B---then I'd not declare time whether I was the official responsible for the call at 2B or not. I'd still see the appeal occurring.
If the defense did not immediately make such an appeal before time is called, they still retain their right to appeal when the ball becomes alive. Still, it's likely to do them little good if the substitute runner returns to touch 2B during the dead ball situation---a right he also retains.
I've not seen your scenario addressed anywhere by specific caseplay, but that's how I'd rule based on the existing wording and my understanding of the rule.
Just my opinion,
Freix
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