No
All that the return spring does is to pull the idler back off the belt so it does not get damaged & the belt has no tension so it can slip on the engine pulley .
If the idler is bouncing then something is changing the tension and usually it will be a bit of crud stuck in the V of a pulley.
Bits of branches get caught then flattened down into the V and are hard to see.
However if you remove the belt and lay a long screwdriver in the V so it touched the pulley about 1" back from the tip of the blade then spin the pulley, and crud will cause the screwdriver to skip.
Some pulleys are made in 2 pieces riveted or welded together and these halves can split apart and that is also hard to see .