You can, since a laptop can still run a LAMP stack, or depending on your specs, perhaps a cPanel or Plesk server. But you will need a good room for temperature control and a good ISP.
Some might not recommend it, but for me I would consider it. Using this method, I really do have full access to the server, since it is within reach. When something goes wrong, I can personally fix it myself without having to wait for a tech staff from a DC to do it. But I agree, the performance wouldn't be that optimal, since being in a DC means more power and security.