I've got the Sys 1 classic version of this, so it might not hold true if you are looking at the Tloc version.
Yes, both to the raised panel bits and the Whiteside spiral ones, though on those you do have to find a spot where the lid ribs won't hit it. The raised panel bits are going to chew up a lot of real estate in there, though. I've got so many bits in there that there's no room for the raised panel ones.