This assertion has been disputed. I think it is correct; for Mélas, confined between the Bormida, the Tanaro, and the Po, was unable to recruit for his army, barely able to maintain a communication by couriers with his base, and he certainly would have been obliged to cut his way out or to surrender in case he had not been reinforced.
The capture of Paris by the allies decided the fate of Napoleon; but he had no army, and was attacked by all Europe, and the French people had, in addition, separated their cause from his. If he had possessed fifty thousand more old soldiers, he would have shown that the capital was at his head-quarters.
The inferiority of an army does not depend exclusively upon the number of soldiers: their military qualities, their morale, and the ability of their commander are also very important elements.
When the fractions of an army are separated from the main body by only a few marches, and particularly when they are not intended to act separately throughout the campaign, these are central strategic positions, and not lines of operations.