No, the shorter draw doesn't create a stiffer arrow. But you have an extra 1-1/2" of shaft, and if you cut that off it will create a stiffer arrow.
I'll give this a try - hope that I make sense, and that I've got it right....
Actual arrow spine is measured by hanging a weight in the center of a shaft supported at each end 26" apart for all arrows regardless of length.
Most arrow charts assume that you are using a 28" arrow. So two arrows that each spine the same might act very different if they are different lengths. The longer arrow will act weaker.
Cut an arrow shorter than 28" and it will act stiffer. Leave it longer and it will act weaker. Both of those are true regardless of your actual draw length.
Increasing your draw length of course increases the draw weight, which then requires a stiffer shaft. It also increases the "power stroke" of the bow, and that will have some impact on arrow requirements as well.
Check out and play around with Stu's Calculator to get a good idea on how all the different variables interact with each other.