Doch. Fret number, combined (obviously) with scale, does matter.
Fret Position Calculator | stewmac.com
^ Fret positions for a 20-fret, 28.6" fretboard. Now subtract the distance between last fret and nut (19.592") from the scale length (28.6"). Result: 9.008", which is the (nominal, uncompensated) distance between 20th fret and bridge. Basically the pickup area.
Fret Position Calculator | stewmac.com
^ Fret positions for a 21-fret, 30" fretboard. Same subtraction (scale minus position of the last fret relative to the nut - in this case 30 - 21.081) gives 8.919". Which, again, is the distance between the last fret and the bridge.
Now, 9.008 - 8.919 = .089". In other words, replacing a 20-fret 28.6" scale neck with a 21-fret 30" scale neck, on the same body, will require an adjustment of less than a tenth of an inch, which is probably within the travel capabilities of the saddles of an adjustable bridge.
QED.
If you think about it, if you have two necks of same scale (say 34") and different number of frets (say, 24 vs. 22 - again, with no overhang, so as to keep the comparison apples-to-apples) you can't install them on the same body without putting the bridge in different positions. Because, with each neck, the section of scale length taken up by the fretboard changes (longer on the 24-fretter), and so does, inversely, the pickup area (shorter with the 24-fretter). Which fact, alone, proves mere scale length doesn't, and couldn't, tell the whole story.
Conversely, if I modify a 21-fret 30" neck, putting the nut where the 1st fret formerly was, I get a 20-fret 28.316" scale neck: if I then use it to replace a 20-fret 28.6" scale neck, I'm close enough for rock n' roll, with saddles taking care of the difference.
(Uh, I'm forgetting sumthing, what was it? Ah: )
Period.