Resting pancake batter improves texture. I think the rise is better and the pancakes less chewy.
Double-acting baking powders work in two phases; once when cold, and once when hot
When you initially mix the baking powder, you will get bubbles, but this does not mean the baking powder is used up. You still get leavening from heat activation.
The King Arthur Flour Baker's Companion suggests resting is about lumps, which you will have because of gentle handling:
If you have time refrigerate the batter for an hour or so, which allows lumps of flour to slowly dissolve, and makes for a more fluffy flavorful batter.
In Keys for Good Cooking, Harold McGee suggests trying to have things both ways:
Prepare most unyeasted griddle cake batters an hour or more before cooking, to give the flour time to absorb moisture and produce a velvety texture... Refrigerate for rests longer than 2 hours. Withhold baking soda or powder and/or beaten egg whites and add just before cooking to maximize their leavening power. Whisk powders with a little flour first to help incorporate them evenly.