Yes you can place a pan on a griddle and cook in the pan however it's not a very efficient way of cooking food in the pan as it will take longer to heat the pan up enough to cook the food in the pan.
If possible just cook directly on the griddle which will cook the food more efficiently and without having to wait until the pan heats up enough to begin cooking the food.
You can also get an electric portable hot plate if you do not have a stove and the hot plates can be bought for as cheap as $10.00
I've tried cooking in a pan on a griddle and it did work but it took longer to heat the pan up enough to cook the food in although it did work.