The short answer as @Huisman said is yes, the cart will likely still need to be Listed (Listed is the correct term for approved, compliant etc. Not super important, but correct).
As you alluded to, there are exceptions based on the input power to the device. I don't know which standard golf carts are evaluated to, my experience is in Industrial Control Equipment. In ICE, for instance, devices which are powered by Class 2 power supples have most, if not all requirements waived:
Furthermore, a benefit of using the power supplies that have received
the Class 2 approval is that the output has the same Class 2 safety
level. When applying for safety standards approval for the equipment,
in some cases it is not necessary to obtain safety standard approval
for the connected device (load) when the device (load) is connected to
the output of a power supply that has received Class 2 approval.
The limited output voltage and power delivery capabilities of Class 2
power supplies are recognized to be of lower risk to fire initiation
and causing electrical shocks, which allows for lower cost wiring
methods to be employed.
In your case, the charger and battery will very likely require testing. Depending on what testing the battery has already undergone, you may be able to waive some or all testing "downstream" i.e. the rest of the cart.