When a laptop running Ubuntu 20 does not have battery, can you simply turn off the power supply to shut it down?

During shut down, many things happen, including properly writing out data cached in the computer memory (RAM) to partitions on disk and closing these partitions. That is why a system should always be properly shut down before powering it off.

Powering off the system without shutting it down should be avoided at any price. This may or may not cause heavy damage to the file systems on the partitions, breaking the entire system beyond repair.

Unpowering a system that is in a sleep state is also not appropriate. A system that is in a sleep state has all data of the current session stored in RAM, and thus continues to use very little power to preserve the data stored there. Also with sleep state, data volumes are not closed. The idea is that the system resumes exactly where it left off when put out of sleep mode. If you now unpower the system, that RAM is lost, and the system has to reboot fully, and thus might encounter a file system that is damaged.

In summary: If you can leave the laptop on AC power, you can put it to sleep and quickly resume later. If you need to take it of AC power, your only option is a proper full shutdown.

All other attempts entail a risk to break your computer.