Does LUKS also encrypt free space?

The standard recommendation, is that you over-write a disk/volume with random data before you setup luks. The Ubuntu installer will even offer to do this for you if you select the Expert mode. I don't believe the latest version will do this by default though, but I haven't actually tried it. This is often skipped/ignored because the process will take a long time.

But no, luks does not automatically fill or over-write blocks when it is setup.

Using the psuedo random generator in badblocks (badblocks -c 10240 -wsvt random /dev/<device>)is usually considered good enough and suggested as a good method to wipe a volume by most LUKS guides and HOWTOs.