I am going to have go with a failing master cylinder because of this:
The pedal will go all the way to the floor.
Even without power assist (i.e. with the engine turned off), the degree of brake pedal travel should not be effected. The vacuum booster only serves to reduce the amount of force required by the driver to apply the brakes - it does not limit/reduce push rod or master cylinder piston stroke.
If the master's seals/cups are failing - and the brakes are applied - the result will be insufficient pressure developed at the master's outlet ports and in the external hydraulic circuits. Additionally, the piston will offer reduced resistance to the push rod/brake pedal.
Without normal pressure/resistance, the piston can more easily be forced into the master's bore. If the internal seals are worn bad enough, the piston can go right to the end of the bore.
A vacuum booster is just a sheet metal shell that contains two chambers which are separated by a flexible diaphragm - which offers very little resistance to application of the brake pedal.
There is a push rod that goes from the brake pedal arm, enters through the back side of the booster housing. Inside the housing it passes through the diaphragm and operates the control valve. It then exits at the front of the housing and extends into the master cylinder.
Bottom line is: if you have excessive pedal travel, it is because you are not developing design hydraulic pressure in the braking system. This could be caused by a failed MC, leaks in the external circuits or air in the system - but not by a malfunctioning vacuum booster.