No.
Ball is dead and a substitute can be put in immediately.
Since there is no rule against a runner being assisted when the ball is dead there is no reason why her own teammates could not carry her around if there where no subs available after an over the fence HR.Two follow-ups: What if the team has no available subs?
And is this also true of any dead ball play? What if a batter hits a home run and she (or a runner on base) hurts herself and can't get around the bases all the way? I remember that video from a few years ago where the opposing team carried the hitter around the bases, but is that even necessary?