It still stops ... until it doesn't.
A number of years ago I had bought a well-used 1878 [EDIT: Make that 1978 /EDIT] full-size Cherokee. Got it home, did a bunch of work on it, got it registered. At that time, anything more than 10 years old in Connecticut required a safety inspection by the state, and it passed that.
Less than two weeks later, in heavy stop-and-go traffic, a woman in front of me stopped suddenly. I slammed on the brakes, the peddle went to the floor, and I stopped with the snow plow rig firmly embedded in the trunk of the woman's Honda Accord. Fortunately, I wasn't moving more than about 5 or 10 MPH before I hit the brakes so there were no injuries, but it could have been ugly if the brakes had decided to fail under other conditions.
Doesn't matter if you only have one vehicle. You also only have one life. Risk it all you want, but the person you're going to hit only has one life, too, and you have NO right to risk the lives of other people by driving around in a vehicle that you KNOW has a problem with the brakes.