Try libgphoto2 to control cameras. I know that Nikon 1 J series are mostly supported. It can capture and fetch at the same time. But a lot of the time, there is an unavoidable delay because fetching the photo means transferring it over the USB cable and that takes time, especially using the old USB2 speeds.
A better route might be to script it so that, say, 100 frames are captured and stored on the card. Then the capture pauses as it batch downloads them. This might overall be faster than saving as you capture.
Many camera control protocols do have a 'live view' option. But the live view is usually (a) just a thumbnail and (b) not subjected to the same ISO/color/etc. settings that the final photos are.