No, a failed brake vacuum booster will cause a rock hard pedal and take 5 times the distance to stop the vehicle.
A pedal that goes to almost to the floor or to the floor, but there is no brake fluid loss, is normally an internal failure in the master cylinder, where pressure bypasses a weakened internal seal and instead of fluid and pressure being sent down the brake lines, it just bypasses itself thru the weakened seal:
If you have 4 pairs of vise grips you can confirm this fairly easily. On each of the flexible rubber brake hoses at each wheel, lightly clamp each hose about midway up. now test the brake pedal. If the pedal still goes almost to the floor as before, then you have confirmed the master cylinder if bad.
If, by chance, the pedal is nice and firm, then starting at right rear(RR), remove clamp and test pedal. Repeat at each wheel until you find the one that when clamp is removed the pedal goes almost to the floor. It will either be a faulty brake hose or brake caliper at that specific wheel.
But odds are that you have a faulty master cylinder