The generator would have to be capable of absorbing the power provided to it by the turbocharged engine. Generally, in an OEM application, the generator is going to be sized appropriately for the engine it's mated to. So, for example, if an engine can provide 100kW of power at 6000RPM, the generator will be sized to convert the mechanical energy to roughly 100kW of electrical power. If you turbocharge the engine to the point where it makes 150kW at 6000RPM, that doesn't automatically mean the generator will be able to convert that to the equivalent electrical power. I think it's safe to assume that in the case of the 3G Insight, the engine and generator are pretty closely matched.
Of course, a properly engineered product usually isn't on the ragged edge of self destruction (except maybe in the highest performance products), and so there's a factor of safety which can be taken advantage of to further increase performance, but often at the expense of reliability. So how would that look in our cars?
1) Potentially allowing the generator to be more heavily loaded across a certain rev range, in other words, generating more electrical power at a given RPM. If that can be done, then turbocharging the engine would help.
2) Increasing the redline of the engine so that the generator can spin faster and generate more electrical power. A turbo could help here if engine power tapers off as it approaches redline. This is particularly dangerous without doing a proper analysis of whether the generator can tolerate the forces associated with higher rotational speeds.
Lets say that one of those methods work, and now we can generate more electrical power. Well, what can we do with it? If our traction motor can't handle the additional input power, and/or our batteries can't take a higher rate of charge then the whole thing is pointless. In a hybrid system such as ours, every part of it has to be considered.
I should point out that there's an exception that immediately comes to mind. I live in the Denver region, which is a mile above sea level, which means the air is thinner, and thus engines make less power here than they do at lower elevations. So, I could theoretically turbocharge my engine to the point where the boost pressure is equal to what it would be like at sea level, and therefore could make the stock amount of power. That doesn't sound super cool, and it would only be useful to people living at higher elevations, but to those people, the increase in power would be noticeable and appreciated.