Definitely possible. Have the player change to a datablock that has references to other sound datablocks that are using a quieter profile. This covers jumping.
However, when it comes to guns and bullets, you would have to modify each and every weapon and projectile to have this functionality. You wouldn't necessarily need new image/projectile datablocks, if you don't use the states/datablock values to have the engine do sounds for you. You'd have to write the sound functions into onfire/onexplode, and have them play a certain sound depending on the condition.
So yeah, while possible, not exactly fun.