Rather than removing the memory card each time to extract the images, can we simply leave the USB cable attached to the camera?

Certainly, but as always, there are some slight complications. The camera will go to 'sleep' between pictures, if the interval is long enough, to save power. If the camera is asleep, it might not wake up when you connect the USB cable to your computer. You may need to cycle the power on the camera, or touch the * button on the DigiSnap to have the camera wake up and take a picture. Once awake, you should be able to download images normally. This means that you will likely have to open the housing door to wake the camera, so there isn't much point to having the USB cable available outside the housing (where it's likely to corrode anyway).