Technically it should help with the lag, because the boost controller is keeping the boost signal from reaching the wastegate actuator, therefore, it is keeping the wastegate puck assembly closed longer which should help with transient response. IE keeps the turbine wheel spinning faster until exhaust is diverted away by virtue of the wastegate pushing the puck open. Exactly how much it helps no one really knows, but I don't think it would help someone with say a stock converter spool up a GT-Q equipped turbo. But it should move the torque band a little lower in the RPM range because boost would be made sooner. I don't think there has been any test results as of yet, but it could be as simple as dynoing a car without one with the boost set at level A, then installing the boost controller, leaving the boost at level A and retesting. The dyno graph would verify the transient response via torque readings. Or if you could data log boost with a FAST or XFI, that would verify it too.
It should help the turbo spool faster. Think about it like this, under normal operation, the wastegate actuator sees boost pressure as soon as you go WOT, this starts the actuation process and immediately slightly cracks the puck open from the face of the turbine housing. This starts the control/slowing of the turbine wheel, once the set spring rate is reached, the valve would be fully opened and turbine wheel speed should be stabilized / controlled.
HTH a little.
Patrick