Unfortunately, yes, your player can get injured in a walkover. Even worse, because injuries happen when a foul occurs, and fouls occur more often in a walkover game (yes there shouldn't be a game, but there is!), injuries are more likely to occur in a walkover.
Which makes allowing walkovers even worse in my opinion.
I assume the 24 minutes is standard for an injured player, since minutes played in the box score of a walkover never correspond to what happens in the play by play.