Interesting questions!
I just strummed my Special and the PS 30th CU24 back-to-back. I should mention that I lucked out with my CU24 - it sounds beautiful, and has a nice resonance.
The Special seems louder, especially in the midrange and treble when it's strummed acoustically. But not all that much louder, only a little bit louder! And the perceived loudness might simply be the result of a different tonal balance and the resonant peak I'll get into in a moment.
My thinking is that a true acoustic guitar is so fundamentally different from the Special that (for me) substituting it for an acoustic would be out of the question. And it's certainly not loud enough to substitute for an acoustic unless you basically don't care what a real acoustic sounds like.
The semi-hollow construction creates a resonant peak in the frequency response.
A resonant peak occurs just at the break point where the high frequencies start to roll off. It's typical of any instrument with body cavities, and you mostly perceive it in the upper mids, giving the instrument a slightly more vowel-like sound on certain settings when it's amplified. It's there but more subtle on the bridge pickup alone, but it becomes much more noticeable as you switch to the 2,3 and 4 positions, and there's noticeably more resonance and roundness in the neck pickup as well.
However, the Special's resonant peak is less pronounced than the resonant peak on a true hollow body guitar, or even a dual-chamber semi-hollow like a 335.
Hopefully this helps a little. But a recording is worth a zillion words, and this one from PRS does a very good job of showing what the guitar does: