I don't see mention of what year your Chinook is, but the overcab face looks exactly like mine in the photos (mine is a 1999). Maybe yours is a 1997 or so? If so, I can tell you what it's made of as I have had mine down and on the shop bench.
Essentially, it's made of thin molded fiberglass, covered by glued-on headliner fabric. There are some wooden stiffeners (around the doors and such) which you can see by poking your head into the lockers. The bottom (floor) of that whole overcab locker (on mine at least) is a 3/4" plywood board covered in the same hull-liner type carpet that the overhead of the whole Chinook is. That board is basically at the level of the top of the little bulge you can see running along just below the cabinet doors of the overcab.
Edited to add: Wait, I just noticed your green circle. I had a bunch of construction information here but I'll move it to the bottom of the post just in case anyone wants to see it later.
Duh, I missed that green circle on first look! So if you are screwing into that face, you will be going through just the thinnish fiberglass of the overcab piece (totally separate from the outside Chinook shell), then air, then possibly the thin downturned Ford steel flange at the aft end of the overcab (if screwing horizontally this does not connect to the outdoors in any way; it's just a single layer steel flange). Or if higher up on that bulge you could catch the edge of the 3/4" plywood overcab piece. On my Chinook there were no wires in that area, btw, except for way over on the sides where the pillars are, and then they were way forward (they go into the headliner). You would have to use very long screws to hit them (inches). In your photo that overcab piece, and even the arrangement of the various doors and TV etc. look just like mine (early 1999). I even had the same telephone

"It's for you!"
PS: Hang onto that couch like gold! Later Chinooks (mine) had the "three hump" couch and at least in my opinion that thing is super uncomfortable, especially as a bed. I modded mine and used sections of a couch from another RV that look almost exactly like yours. Ahhh, flat bed.
PPS: I would think an upholstery shop would be a lot more likely to screw it up than you. They aren't going to have any idea what's behind there, and probably don't care as much as you, plus they will be working to a schedule.
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Info cut from above after I noticed your green circle. Might possibly be of interest so putting it here:
The top in-turned rim (where I don't think you'd be putting curtains) is screwed into the ceiling of the Chinook (essentially gripping the inner fiberglass skin of the roof structure) and the bottom rim is, IIRC, held up by screws and the wooden trim strip (~1/2" x 2" of oak that matches the cabinets on my Concourse). That strip is in an area where there is a doubled inner member on the underside of the steel Ford cab roof. As you come back into the bottom bulge area closer to where it makes the corner to go to the vertical face, then there is more airspace (the Ford cab roof is up there, but there is no rib to come down and meet the fiberglass). I imagine that's why Chinook joined their two moldings in that particular spot (cab headliner mold, at least on mine there is a Chinook headliner not the Ford one), and overcab cabinet mold.
As you get out toward the edges of the cab (where the vertical pillars are) then the overcab curves aft and in that area there is just the 3/4" plywood bottom of the overcab above the fiberglass of the cabinet module. I think that's all under the vertical pillars though.
I can't see anyplace where you would be able to run the screws into the great outdoors, unless you used *really long* screws that went through the fiberglass molding, through air, and then through the metal Ford roof (although even then you'd be under the Chinook outside overcab fiberglass, which, if that was not sealed you would already be getting water pouring out the rear of your overcab locker I believe).
There is a single thickness steel downturned flange right at the aft end of the overcab (basically the very end of Ford's chassis cab). I suppose it's possible you would contact that when you drill. But that doesn't lead outdoors.
The thin fiberglass along can probably hold a curtain track, especially if you are not hanging 200# of curtains, and of course better if the fasteners are in shear. So in short, if you are just using short screws (say 1/2" or so) you will likely only be going through the thin fiberglass of the overcab face/bottom shell.
I do have some photographs of this on another drive. But not right with me.