I'm thinking you'll want to get a second blower. One would be inside the room scrubbing the air with the carbon filter, however many cfms required for your scrubber.
The other blower needs to be on a separate ductwork circuit, carrying air over the cool tube and exhausting the portable a.c. as well. You could pull air from outside, filter it for bugs and stuff (not carbon filter), through the cool tube to pick up heat, and back outside it goes, along with ac exhaust.
The problem with your drawing is that you are moving the air conditioned air out of the room. Expensive.
I've never run a cooltube, but I'm pretty sure they need to be on a separate duct line if you're going to be using a.c. in the room, or else you're just wasting $ on ac...
You need more opinions lol
Oh I see that you have two blowers, cool. I think they'll need to be separate, but you should confirm this.