A leaking brake booster will not cause the pedal to drop to the floor - all the booster does is reduce the pedal pressure required to create a given amount of hydraulic line pressure - a failed/failing/leaking booster will cause the pedal to be higher & harder - try depressing the pedal with the engine off and see what happens.
Here's a quick & easy way to test the booster...
With the engine off, depress the brake pedal half a dozen times, with each press the travel should be reduced, and after the third or fourth time, the pedal should be stopping at about the same point - now hold the pedal down firmly and start the engine - as soon as the engine starts and develops vacuum in the intake manifold, the pedal should drop an inch or so, and then hold steady.
There is no fluid in the booster, only engine vacuum and air, if it's leaking, it's air leaking into the vacuum chamber, and that makes the booster less effective or completely ineffective, which is what you would have experienced when the above test was performed with the engine off and there was no vacuum.
The pedal sinking to the floor is a fluid leak, either external, which will cause a fluid loss or internal to the master cylinder, in which case, there will be no fluid loss