Let's say that d'Erlon I Corps participate in the Battle of Ligny and Napoleon manage to destroy the main of the prussian army and manage to capture Blücher.
-Wellesley's reaction ?
-Prussian command's reaction ?
-Would Napoleon have detached Grouchy to pursue what remain of the Prussians?
If the Prussians were fully defeated, Wellington would escape from Belgium. He knew that the only hope to defeat Napoleon in open battle was with the Prussians, without them, the cautious Arthur Wellesley would never give battle in Waterloo.