I don't have one of their pocket organizers ,but I do have an organizer in my pocket.
Like you I want to be able to draw my knife without taking the organizer from my pocket, and this is absolutely something you can do.
It depends on the organizer you have the size of your knife and the size of your other items, but having to take the organizer out first is not an absolute inherent trait of pocket organizers across the board.
I have prioritized drawing of my knife pen and mini multitool without organizer removal with my flashlight just being clipped to my pocket, and I can do it very easily with my items and the organizer I carry.
The rest of my items I'm fine with accessing with the organizer out of my pocket.
I would recommend taking another look on their site while keeping in mind the things you'll be putting in it, they seem to have a decent variety of models / options and there may be one you can draw your particular knife or flashlight from without removing it.
I'd also suggest looking at yellow birch outfitters, I don't know if they'll have what you want but I've had one of their organizers in my pocket every single day for almost 3 years now and can't recommend them enough.