Do downloads continue when lid is closed?
Nope. When you close the lid, your Mac goes to sleep and stops all current downloads. If you have a downloadmanager, it will pause the downloads, but it will not keep downloading the files.

If you would like to work with your lid closed, I suggest you connect an external screen or try software like InsomniX, which will keep your Mac awake when the lid is closed.

Also, it might be worth trying extention No Sleep.