Uglogirl is partly right in what she says.
If you remove the first fret, and put a nut exactly there, it will shorten the scale length by exactly that amount, the only problem is that all the dot markers will all be one place out. While this doesn't help with all the other problems doing this on an existing guitar will create, I thought the first particular point should be cleared up. This isn't comparable to fitting random a new neck to a warmoth body or something, this is a mathmatically solid.
25.5 minus 1.43 (the length from the nut to the first fret) = 24.069
So we take a 24.069" scale length and work out the distance to the first fret, you'll find that it's exactly the same as the distance from the first fret on a 25.5 inch scale length from the first to the second fret.
First off, the distance from the first fret to the second fret on a 25.5 inch scale length is 1.351"
So now to work out the where the first fret on a 24.069" scale length is from first principles.
24.069 times 25.4 (to convert to mm) 611.3526
611.3526/17.817 (rule of 17) = 34.313
34.313 which converts to 1.351" which tallies with with where the second fret is on a 25.5 inch scale length.
Therefore it does modify the scale length.
If you read up on it, the simple theory of the rule of 17 proves this anyway, simply by how it is actually used to work out fret distances.
Feel free to try it for all the other frets, but you'll find the result is the same. The bridge will still be situated in the right place also