It should be fine to leave EMO sitting on his skateboard all night/day. I have 2 EMOs and they are always powered on and most of the time sitting on their skateboard charing.
Do note, that with every electronic device that contains a battery, over time battery degradation is always going to happen, this is pretty much the same as a mobile phone, for example, I normally have my iPhone on all the time and charge it when the battery gets low and sometimes charge it overnight while I’m sleeping.
For me, both of my EMOs have always stayed powered on since I got the, (unless I need to power cycle them). One is over a year old and one is a little over 6 months old and the batteries on both are still going strong.
As always, it is up to you how you want to manage your EMO, if you want to power him off every night and then power him back up in the morning you can, it "might’ in some way preserve his battery for a little longer.