The resonator box inside the fender is fairly easy to take out, and does allow slightly more air to enter the filter. I removed it on my Corolla to install the CAI and also on my brother's Caldina GT-T (3S-GTE) a few weeks ago and we noticed that it didn't lag as much when getting on boost.
As for the second resonator closest to the throttle body (after the air filter), it actually does more than just silence the intake. In 98% of applications, it's designed to match the particular characteristics of the engine and can have a huge effect on the smoothness of the power delivery and bottom-end torque. Most of us remove this part when we replace our intakes with a nice shiny aluminium pipe and pod filter, but by doing this we are actually reducing power.
As proven in real-life tests, removing the inlet resonator will see drops of around 3kW-5kW throughout the entire rev range, with things starting to return to normal around the 6000rpm mark. This has been tested many times on a dyno by technicians, and manufacturers such as ARC now even have inlet resonators side-branched off some of their inlet systems. You won't notice these losses during driving, but will on a dyno.
A larger inlet resonator will produce slightly better top end results, while a smaller inlet resonator will see slightly better performance in the lower rev range. Bear in mind that you must have a clean air filter or you won't see any gains no matter what you do.
So at the end of the day, if you have the option to keep the inlet resonator closest to the throttle body, do it. If not, then it's no great loss, but a loss nevertheless
EDIT: This is the photo I took after removing the resonator box in the fender of my Corolla. My brother's Caldina fender resonator was almost exactly the same size, so I suspect they'd be a very similar size on Camrys: