Mark.
I have not any figures on the acceleration subject so it has to be guesswork, may be Maciek has some. Anyhow as you rightly stated the VIICs have fixed propellers, as such it has bad efficiency in some ranges. If the vessel is at 0 speed and should increase to say 17 knots, you start the engines and stir up a lot of water for the first 100 m. Then the propellers gradually improves and you increase the revs to max. and you might achieve 17 knots at some 300 m. So a guesstimate of 400m to obtain full speed of 17 knots. Which means an acceleration from 0 to 17 knots or app 31,2 km/hours over 400m. This is a pure guesswork from my side and take it for that.
Your simulation of an engineacceleration 0-350 rpm on 7-8 seconds seems not to bad to me with all the components connected.
Roots blower.
I believe the Roots blower is not an ordinary supercharger but rather a booster which is needed for getting extra max. output. The difference being as an ordinary turbo supercharger takes the thermal waste energy from the exhaustgases and thus improve both the output and fuelconsumption, the Roots blower require energy which is taken directly from the engine via the camshaft drive. Thus it takes a higher specific fuelconsumption to boost the engines, but it was at that time a common way to get more output of the engines. MAN submarine engines had a first generation turbocharger called the Buchi system and utilized the thermal energy of the exhaustgases.
Thus you did not want to run the Roots blower unnecessary as it took energy from the engines. The GW engines operated as normal aspirated engines up to 390- 400 rpm I Guess, then you had to make use of the Roots blowers to get more output. At lower revs like below 390 the blower did not contribute anything in fact it took only energy from the engines for doing nothing, moreover it is not an advantage to have two big rotating weights connected to the camshaft drive wear and tear, torsional vibration. etc. So it was definitely disconnected at lower revs like 390 rpm.
Tore