hybrid vehicle DC voltage boost
You could say this system already works. I have a standard full-hybrid. Where a petrol engine works in parallel with the electric motor to move the car forward.

This is also similar to various diesel-electric locomotives, which use an engine to generate electricity which powers a motor. There are some shunting versions of these which use a generator in parallel with a battery pack so that their instantaneous power can be higher than just the engine or the batteries on their own.

Then there are also machines such as the River Simple hydrogen car which uses a hydrogen fuel cells to generate electricity from hydrogen which it then stores in batteries to give good acceleration. Replace the hydrogen fuel cell with an internal combustion engine, and you have your design.

The thing to notice here is that all the systems work in parallel. This is because it is a lot easier to integrate the two power sources in parallel rather than in series. If you have an engine in series with batteries, the voltage out of the system will depend on the power out of the engine. Engines are very slow to respond to changes in loads. Suddenly removing the load will cause the engine to spin up and cause the generator to provide very high voltage for potentially a long (5 seconds or more) time. If the generator is in parallel with the batteries, the engine will always see a load as the external load can be replaced with a load to charge the batteries within milliseconds with ease.

To answer your question: Yes it can work, and indeed does in various production cars (all full and plug in hybrids), as well as locomotives (diesel-electric) and famously on the BBC program Top Gear with the Eagle i thrust.

The important fact is WHY do you have an engine there? You seem to be planning on having an engine there to over come high power/current demands. That won't work too well, as engines are very slow in getting up to speed compared to what can be done with an electric motor and a good battery supply. If you look up the fastest accelerating cars, the world record of 0-60mph (0-100kph) is held by a fully electric car for a reason.

So, in summary; you idea works and is in use today. But for the purpose of extending the range or improving the power delivery of the machine. Putting an engine to over come current spikes is a bad idea due to the slow reaction time of an IC engine.