That depends on how Toshiba engineered it. You'll only find out when it happens, I'm afraid.
But you can try already now what happens if you remove the battery. Does it still run? Then it will also run if you remove a dead battery.
If it doesn't run without battery, however, only Toshiba knows if it will run with a dead battery. For that, you'll have to wait and see.
<font size="5">I have a three-month-old Toshiba Laptop with a battery already installed at the time I purchased it. I keep it in my house plugged into an electric outlet. My question is this: If my battery dies out can I still use the Laptop plugged into the electric outlet? Would I have to remove the dead battery or can I keep the dead battery in? Would keeping the dead battery in cause any damage to my Laptop? Thank you for your response. user470