It's almost hard to imagine a time when cars didn't have hydraulic brakes, but the automobile existed for about 30 years before Duesenberg installed the first hydraulic system on a production car. Vacuum boosting helped ever faster and heavier cars stop with some modicum of safety -- something those old cable-operated brakes could never hope to do.
A vacuum brake booster works by using engine vacuum sitting in one side of the brake booster chamber to help pull on a diaphragm attached to the hydraulic brake master cylinder's piston rod. Without the consistent supply of vacuum drawn from the intake manifold, the brake booster would lose its ability to assist in activating the brakes.
Depending on where the brake booster taps into the manifold, and how close it is to the leaking manifold gasket or other vacuum leak source, it might be possible for a very large vacuum leak to cause a loss of brake system performance. However, to completely lose all braking assist, the leak would probably have to be enormous -- enough so that the engine would barely run, if at all. So yes, it is possible for a massive vacuum leak to affect your power brakes; but at that point, you'd probably have a much harder time getting the car to start or idle than getting it to stop.
