1) Wellington would never have faught the battle if he had doubted Blücher's intentions. The commanders were in contact all the day. There are a lot of myths around. Both Wellington and Napoleon were fully aware of the Prussian movements.
2) Grouchy did not have a chance to get to Waterloo. Wrong side of the Prussians and a river and a Prussian corps seperating him from Napoleon. He forced his way over the river (at Vawre), but it was too late.
3) If anything Blücher did the right thing all the time, as he did the year before when he simply decided to ignore Napoleon and walk directly against Paris. But Blücher would have faught in vain--was not really a match for Napoleon as shown at Ligny--if not for his deal with Wellington.
PS: It was perhaps rather immaterial who won the battle. Napoleon would have lost in the end. It was a matter of Napoleon denying the old soldier's fate: Old soldiers never die, they just fade away. A fantastic finale for both Napoleon and Wellington who never faught another battle. They were certainly not forgotten by history. Something similar today? Well, Zidane's exit from football. He will always be remembered because of this last incident in the final a few years ago.