A week's grace granted by Napoleon, or a week gained by the Russians on their actual marching time, would have altered the whole situation in Bavaria--and Prussia would have drawn the sword against France to avenge the insult at Ansbach.
On October 10th Hardenberg informed the Austrian ambassador, Metternich, that Frederick William was on the point of declaring for the allies.

Nothing, however, was done until Alexander reached Potsdam, and the first news that he received on his arrival (October 25th) was of the surrender of Ulm.

Nevertheless, the influence of the Czar checkmated the efforts of Haugwitz and the French party, and kept that Government to its resolve, which on November 3rd took the form of the Treaty of Potsdam between Russia, Austria, and Prussia.

Frederick William pledged himself to offer the armed mediation of Prussia, and, if it were refused by Napoleon, to join the allies.

The Prussian demands were as follows: indemnities for the King of Sardinia in Lombardy, Liguria, and Parma; the independence of Naples, Holland, Germany, and Switzerland; and the Mincio as Austria's boundary in Italy.[35] An envoy was to offer these terms to Napoleon, and to bring back a definite answer within one month from the time of his departure, and in the meantime 180,000 Prussians prepared to threaten his flank and rear.