We are using some Avigilon 5MP IR bullets and domes to capture license plates in parking and driveway areas and they do general overview double duty as you noted your customer wants to do. One thing I have found is that, as others have mentioned above, adjusting to a shorter exposure length makes a significant improvement in low lighting conditions, though there is definitely a trade off in a darker image. Depending on location, we're using 1/100 sec or 1/125 sec settings. We have found the 1/250 sec setting to be too dark for night use.
Another thing I've found is that pixels per foot is really the primary deciding factor on whether the Avigilon cameras (and others we use) can reliably capture license plates. In all instances where we are capturing license plates (successfully) with the Avigilon cameras, we are using the 9-22mm lens option. During daylight hours, our capture rate at ~100 ft. distance to target is 100% at maximum zoom (~126 ppf according to the handy IPVM calculator) and 7 images per second, and we can reliably (>85%) capture tags out to at least 175 ft. (~72 ppf) during the day. Under optimal lighting conditions we can capture out to 200 ft.
In low light conditions that drops to around 70% at 100 ft. when the cameras switch to night mode, and less than 50% at 125 ft. The greatest challenge when the devices are in night mode is that even at faster exposure times, the tail lights, tag lights, and brake lights can "blind" the camera against a detailed image capture.
Our experience has been that the Avigilon IR bullets (with adaptive IR enabled) are much more effective than the IR domes for this application. Nighttime license plate capture rates for our Avigilon IR domes at 50 ft. is less than 50%, and only around 95% during daylight.
Finally, if the Avigilon camera has WDR we have had issues in the past with "ghosting" (motion blur) that made it hard to see details on moving objects. I have not revisited this in a while, and there has been at least one Avigilon firmware update since. On a side note, when we reported the ghosting issue to Avigilon through our integrator, the recommended "fix" was to disable WDR.