Yes turbine drive pressure is the exhaust gas coming out of the engine. Drive pressure is variable on RPM, fuel and boost. You can measure drive pressure just like you measure boost pressure. The more efficient turbos will have a low ratio of drive pressure to boost, so that 1:1 ratio is 100% efficiency, but the GM4 that I measure seems to be about 1.5:1 at 12psi, so like 65% efficient at that boost. The ATT I measure is more like 1.2:1 ratio at 12psi, so like 85% efficient at the same boost.
Turbo works off of pressure differentials. the turbine spins faster as drive pressure increases over turbo exhaust pressure. So lower exhaust pressure from larger exhaust pipe after the turbo helps the turbo spool faster and boost more efficiently by increasing the pressure ratio on the two sides of the turbine.
Edit for clarity: thats two differet ratios I was talking about. One is a boost pressure to exhaust drive pressure for determing efficiency; that is the compressor side vs the turbine side of the turbo. The other is exhaust drive pressure to exhaust backpressure only across the turbine of the turbo.