what are the disadvantages laptop using without battery
While this is not an electronic design question AS ASKED it has implications for designs using Lithium Ion (LiIon) batteries.   

As you know, turning off the power will immediately stop the laptop.

BUT leaving the battery unused can be good for it compared to subjecting it to charge discharge cycles unnecessarily as long as it is stored in a "good" state. 

The best state to leave the battery in is when it has finished constant current charging and has just started constant voltage charging.   This occurs in the 40 to 50 minute range when charging from fully discharged with most LiIon batteries.

Storing fully charged is better than storing empty.