You can, but even with a completely dead battery, unless something other than the battery is the cause, the system should remain powered on with AC connected.  If it's shutting down on AC power, you have an issue with something other than the battery.  
Hello i just now did a Bios diagnosis of my Dell Inspiron 7577 , because for the third time now it shutted down by itself , and it wasn't hot at all. Turns out my batteries life is at 3% .  I'm in the process of ordering one .I need my laptop for work and I don't have any other use in the meantime.  My question is can I remove the battery since it's not  from the  easy removable ones , and use it without the battery? 
Inspiron 7577 Battery