Q:

What happens when battery is fully charged in Ubuntu 18.04? 

I have a MSI GL63 laptop.  Under Windows I can have it all the time connected to the current and the battery does not suffer any damage (affirmed by MSI).  But I installed Ubuntu 18.04.2 for software development and I wonder how the current management works in this system since it does not show the message "Connected but not loading" as Windows does. 
Can I also have connected to power even after charge the battery completely in Ubuntu 18? 

A:

AFAIK The battery charging thresholds are hardware dependent.   There are some notable exceptions, such as the Thinkpad line of computers in which the upper level of battery charge can be set in Ubuntu, but controlling the rate of charge is usually performed by the laptop hardware. 
As a thought exercise, what happens to your Windows laptop when Windows is off, but the computer is plugged into a wall?   Does it 'overcharge'?   Windows is not running (the computer is off). 
If power management is a concern for your computer, consider using TLP

