No, a leaking brake booster itself cannot directly cause the air compressor to go bad. The brake booster is part of the braking system and uses vacuum, not compressed air, from the engine's intake manifold. The air compressor (if your vehicle has one, typically for air suspension or other air-powered systems) operates independently and uses a completely separate system.
A leaking brake booster will affect braking performance because it reduces the assistance provided to the brake pedal, making it harder to stop. However, it won't put extra strain or cause damage to the air compressor. The two systems are entirely separate.
