Those pieces are merely silencers and deflectors IF there is no apparent wireloom or other sensor in place. Water getting into the air intake aside, you should be just fine with it removed. You might also see more underhood dust & dirt, making the engine bay a nastier place to work as time presses on.
One of the first things I did with my old '04 GT was remove the air silencer just ahead of the air filter. Given this is an Accord, I'd say quietness and comfortable refinement are paramount--she might have a littler more noise in the ride now...that's about the only negative I can see from this, unless again, there was some wiring or a sensor involved.