I believe that is correct although the sim doesn't model the shutting down of one diesel visually from what Ive seen in game. With TWOS mod speaking to the Chief will give an option of using all available power for speed (from memory).
The following is quite an interesting read on the subject and the relevant section Ive copied and pasted just below although the pictures it refers to youll have to see in the article:
https://uboat.net/articles/id/54
Charging of submarine batteries:
The submarine batteries must be charged from a source of DC (direct current). Voltage of the DC source must be higher than voltage of the batteries. Terminals of the source and the battery must be connected on the following way: "plus" with "plus" and "minus" with "minus". The charging of the submarine batteries must be as fast as possible. It depends about the cell technology and about the method of charging. The most efficacious method is "UI-method". The method begins with high electric currents, until to cell voltage of 2.4 V, i.e. up to beginning of gas. After that the charging continues with constant voltage and reduction of the electric current. A battery is full charged when the battery voltage and the electrolyte density are constant for a longer period.
The DC source is (the most often) a DC electric machine. The same DC electric machine works as a DC generator and as a DC electric machine for submarine propulsion. The DC electric machines/generators and additional apparatus for the battery charging are located outside of the battery room. When the submarine is surfaced the electric machine is powered by a diesel engine and works as a DC generator and produces DC current for the batteries charging.
Picture 1 shows situation when a submarine is surfaced. DC generators/electric machines (EM/G) are powered by diesel engines (DE). One part of produced electric power from the DC generators/electric machines is used for propulsion of the submarine propellers (P) and the rest of produced DC electric power is used for battery (B) charging. In this situation the diesel engines are full loaded. When the submarine's speed is faster the time of the battery charging is longer, because fast speed needs more electric power. Opposite, when the submarine's speed is slower the time for the battery charging is shorter. In that case, slower speed needs a smaller part of the electric power and the bigger part of the electric power remains for the battery charging.
When the submarine is under surface the diesel engine cannot operate (except in some cases). Then the DC electric machine (powered from the batteries) works as the submarine propulsion engine.
Picture 2 shows situation when a submarine is under surface. The submarine's diesel engines (DE) are out of work. DC electric machines (EM) are powered from the submarine's battery (B). In this case the DC machine/generator works just as DC electric machine, because there is no any production of the DC electric power.