The long answer is maybe. They said some people claim to hear a difference but it is so slight and subjective that it can not be attributed to the truss rod as opposed to the natural variation between two guitars built from different pieces of the same wood. I was told Paul still prefers the carbon rod and that's why it is standard on the Private Stock models.
Makes complete sense. Here's my admittedly subjective and unscientific take on the whole acoustic guitar truss rod conundrum:
I started playing acoustic guitar, and specifically Martins, in the days when they didn't have truss rods, though I suspect that mine may have had the old T-bar reinforcement (evidently during this era some did, some didn't). For whatever reason (maybe it was the truss rod, probably not, but who knows?), there was a characteristic sound to the envelope of each picked or plucked note that is hard to put into words. The guitars certainly sounded very "woody." I stuck with Martins for a long time, and never had one with an adjustable truss rod. I think that for whatever reason, later Martins sound different.
At some point, I switched to Larrivee, Taylor, and later, Collings. All super-nice guitars with different sounds. All had truss rods. The Collings were on a different level from the Taylors and Larrivees, sonically, and I still think of them as very high end guitars.
Something bothered me about the Taylors I had. They were easy to play, mostly sounded great. But there were overtones on certain notes I didn't really love. In my ignorance, I guessed that maybe the bolt on neck construction had something to do with this. My Collings guitars that replaced the Taylors did not have this particular set of overtones.
Fast-forward to the PRS acoustic. With the carbon fiber reinforcement, I was reminded in a certain way of the note envelope I got with my old Martins. Of course, the guitars sound quite different from a Martin, I'm talking about a certain way that the note begins when picked or plucked with the fingers. Is that a result of not having a massive metal truss rod and the carbon fiber? I don't know for sure. I haven't played one with a truss rod! But I liked what was happening an awful lot.
Is this subjective? Certainly. Is it a very tiny difference? Absolutely. Then again, in the studio I make my living discerning very tiny differences. Maybe that's something I'm decent at.
So when it came time to order a guitar in maple to meet certain studio needs, I decided not to mess with that part of the prescription.
Does it make sense that a long hunk of a few pieces of steel (or whatever other metals go into this thing) inset into a wooden neck that is vibrating and contributing to a guitar's tone is going to be audible? I think it does, though one can argue that its effect is subtle compared to everything else in the guitar's construction. Does it make sense that a long hunk of graphite is going to be audible, but perhaps in a somewhat different way? I think so. Again, this may be a very subtle thing.
But we argue about shaving a brace here or there, and the effect of heavy tuning machines vs lighter ones, and on and on. Bone nuts vs composites. Clearly there are a lot of things that affect an instrument's tone.
Graphite also offers something I like a lot, which is that it's extremely rigid, and the neck stays very stable. That's a good thing, too.