No, not during the battle, but after, yes. There is still no differance.
There are many ways that friendship can be effected from a battle. Items will have the same effect as out of uses, so bitter herbs will still decrease happiness, and fainting will also. Pokemon can get happier from battles if they're in an important battle such as the Elite Four or a Gym Leader. As mentioned before, the friendship's effects take place after the battle, or else the game may get confused with Return/Frustration power.