Kiwimagic,
Not quite, they are two completely independent systems.
The wastegate controls boost pressure. The boost source is the inlet pipe across the valvecover, so it is seeing boost pre-inlet manifold. You can see the small line with the nipple just over top of the turbocharger, with a line that goes down to the turbocharger's wastegate actuator. When boost pressure reaches the maximum pre-set in the actuator (by spring pressure) the diaphragm pushes a rod, which opens a port on the turbine side of the wastegate to allow exhaust to bypass the turbine. This creates a self-regulating feedback loop to control boost pressure. Installing a Boost Controller in the line to the actuator fools the actuator, allowing you to accurately raise the overall boost pressure in the system.
The blowoff valve does nothing to control the boost, it just there to prevent overpressure in the inlet pipes or stalling the compressor in the turbocharger. It vents or bypasses the already moving air so that it doesn't build up in the inlet pipes when the throttle suddenly closes. It vents air pre-inlet manifold, using a vacuum line from the inlet manifold. The throttle closing generates vacuum that goes to the BOV. The pressure differential in the diaphragm of the BOV between the inlet pipe & inlet manifold vacuum are what cause it to actuate.
The BOV does nothing to control the boost, it is there to save the intake piping & turbo compressor
Turbocharger lag comes from the inertia of the turbocharger itself, it takes time for the turbine to get the compressor up to speed. It does not take much time for the air to build up, it takes time for the machinery that moves the air to come up to speed