That's how I understood it. (Disclaimer: I do not have access to the schematics nor a description of the theory of operation of the Carlson low-voltage leakage tester.)
Apply a voltage, measure the current. If it's too high, then the capacitor is leaky. The top row of LEDs indicate how much leakage there is, the range of which is not labeled, but you could probably add your own labeling.
Is it a complete replacement for the high voltage leakage testers? No. The voltage matters to really know if the capacitor is OK for the environment in which it much operate. However, if it leaks at a much lower voltage, then it's clearly a bad one.
If I remember correctly, he said that his tester is a safer and less expensive alternative, rather than a direct replacement, for the high voltage testers. Like any tool, it has trade offs, but once you learn its behaviors and how they change with different types and values of capacitors, it may be sufficient. If not, then grab yourself one of the good old high voltage leakage testers. I found a Sprague TO-6 locally (buried in a guy's garage) for a good price. Get them while you can (or build one).