Re: Can the right pickups get Les Paul tones from any guitar?
I'm going to say...maybe. I have several Les Pauls, and with many of them having different construction (long vs. short neck tenons; chambered vs. swiss-cheesed vs. solid; ABR-1 vs. Nashville bridges; etc.) and different pickups, so it's difficult to define "THE" Les Paul tone.
There are a lot of guitars on the market that are 2HB, V/V/T/T controls, 24.75" scale, 22 frets, stop bar tailpiece and tune-o-matic bridge, set neck and maple over mahogany that are NOT LPs, and they're the ones that are going to get you closest. One other criteria that is important to me is having the neck pickup under the 24th fret harmonic. My Ibanez Ghostriders come pretty close to this, even though they don't fit all the criteria, but they are close enough that I can use them interchangeably with any of my Pauls.
Conversely, my G&L ASAT Deluxe is a 2HB (split-coil '59 and TB-4), maple over mahogany, 22 frets--but it is 25.5" scale, bolt neck and this particular guitar has Leo Fender's Dual Fulcrum Vibrato. Ain't even close to the tone of any of my LPs--it's still a 2HB, but it is a unique tone and the springs in the vibrato give it an airy, reverb-ish quality, almost like a full hollow.
So I can argue that every construction detail is important and contributes to the sound of the guitar. It all acts as a comb filter to shape the frequency response. But personally, I try not to get caught up in minutia. It's a simple question of, "Does this work for me?" For me, a lot of times "close" is all I need.
And you are the only one that can determine if "close" is close enough for you and your needs.
Bill