Well locking up the tire don't know. Depends on how sticky your tires are, road surface, and how fast you are going.
I can tell you this, if the master is faulty it will leak and if you hold the pedal down it will fall away. It should stay firm. If you have the wrong brake pedal or master the pedal will have the wrong pedal travel, but you still will at some point generate the same pressure provided you have enough travel.
Your car should have a 1" bore MC, and the power brake pedal. Correct travel should be about an 1" to 1-1/2" and pedal should be firm. If the pedal is hard and you have to push hard to keep the car from rolling in gear then your booster is not working correctly.
The power brake set up has less leverage then the manual setup so your travel is less, but you need the booster to make it up. If their is air in the lines you will have a spongy pedal.
If it was me I'd start by trying a cheap set of brake pads and scuff the rotors see what that does. I would also verify that the caliper pistons move freely. Stuck or sticking caliper pistons is a common problem. I l know is all new, but is easy to verify.