Well it depends on who hits it first. If a bot that usually does well hits it first (it prints out a grudge list, so you can see the order of who it is going after), it tends to greatly lower their score.
Since it will go into blind rage and go after it. Sometimes yes, it has to cross the field and will die. But other times it is right near the enemy, or far enough away that the said robot targets other robots first, but there are no other robots between it and its target (this seems to happen a good amount).
But I saw it get quite a few kills of Shadow, since it didn't care one way or another about dying and just wanted to harm Shadow. Shadow has other problems to worry about usually. So while it ends up dicing up Grudge pretty quickly its lost 50% of its health, which greatly harms its battle.