I've been running a wide format UV coater for 20 years now. We don't use it every day but when we do, we drain ours before leaving for the day. If you leave it too long, the coating chemicals can start to separate after spinning for so long, especially anything with matting agents. You also run the risk of contaminates getting in your coating. You also don't want to leave your rollers pressed together without spinning or you'll create a flat spot. You also, (wow lots of also's, lol) risk running out of coating if you don't have a continuous flow of coating or some sort of sensor that would add when low. Since you're typically running the rollers all at different rpms, you need the lubrication of the coating to prevent the motors from ruining each other trying to run at different rpms.
So, simple answer, no, don't leave coating in it overnight. We try to run all the jobs at the same time, but if we do have gaps during the day, we'll turn the UV light off and just let the rollers continue to spin until we're ready and then drain at the end of the day.