Yes, a master cylinder failure can cause your master power brakes to stick. Normally, your master cylinder is filled with brake fluid. When you press the brake pedal, the hydraulic pressure in your brake system increases, which forces the calipers to grab the rotor or the shoes to engage the brake drums. If the system fails while your foot is on the brakes, it is possible that your system will remain locked in an “on” condition, causing your brakes to stick. Though rare, this situation can occur as your brake system fails to release its components and the brakes remain in an “on” condition. To prevent damage to this system, it is best to have your vehicle taken on a ramp truck to your mechanic.
For more info, see How to Repair Power Brakes in 5 Steps