Does it matter if the executioner extracts a confession from Aryan La Valette?

In the La Valette's dungeons in the prologue for The Witcher 2, if you helped Aryan La Valette escape, he will help you flee the dungeon. There are two ways to meet up with him -- the first is by getting the key to open the locked door in the dungeon, dropping down, and interrupting the Executioner's torture session.

Alternatively, if you ignore the back passage you will come upon Aryan La Valette mounting an escape of his own. Presumably, at this point, he has signed the false confession claiming parentage over the late King Foltest's children.

Does it change anything, plot-wise, if you rescue him from the hangman as opposed to discovering him mid-escape?

It doesn't matter. The plot is unchanged, regardless of whether you meet Aryan in the executioner's chamber, or during his escape.

well.. regardless of what he signs.. you blow up the entire place.. evidence destoryed.. hence, he signed nothing.. im not sure if it was left as an "open" option in the canon or not.. i didnt hear him confessing though.. nor signing anything (he tortured him, 10secs later we were there..)