There are two school's of thought. 1.) All laptops are designed not to over charge the battery, so leaving it in poses no problem. 2.) Some laptops will run with only the power cord plugged in and the battery removed, some won't.
Using a laptop is a must for me as it allows me to use it while laying back in bed due to a disability. Thus a desktop PC really is of no use.
This leads me to a good question: