Nope.
The only way it might possible work is to disassemble everything, and I've never wanted to.
Here's what I do.:
I put the hones in the pockets, the holder is rolled in the pouch after the flap is down, and the guide has one of the ties looped through it to hold it on the outside of the roll.
It isn't pretty, it isn't neat, but it fits in the large plastic bag with the rest of my sharpening gear and stays in one piece.
Good luck.
Greg