As a general rule, yes these work, assuming you only have one character in battle at a time, however it isn't quite an instant victory.
Dominants can be played at any time unless an ability is being resolved (you can't play Angel of the Lord after a Two Thousand Horses draw but before the play) So if you have a hero and your opponent has an evil character in battle you can play Angel of the Lord to discard the evil character.
If an enhancement removes a character from battle (such as shuffle, discard, capture, convert and a few others) it could end the battle, however you can play a card that interrupts or negates the card causing the removal (or interrupts the battle if the card causing removal is in the battle).
Also in either of these situations you could use another ability that adds a character to battle from an active Artifact (like Unknown Nation) a fortress (like Gates of Hell) or a Site (I'm not sure if there are any at the moment, but that can change) or some other ability that is already active. You can use a Dominant or Artifact (or other ability that is active) to stop the rescue, such as Christian Martyr or Unholy Writ
I hope this makes some degree of sense, if not I'm sure someone else can explain it better.
