Does 'du' command count the size of unaccessible folders?

Simply not. Look this example

du -shc *
4,0K    AUDIO_TS
4,4G    VIDEO_TS
4,4G    total
chmod 000 * #don't use this in wrong dir!
du -shc *
du: cannot read directory 'VIDEO_TS': Permission denied
du: cannot read directory 'AUDIO_TS': Permission denied
4,0K    AUDIO_TS
4,0K    VIDEO_TS
8,0K    total

du is an ordinary command running with your privileges and access rights. Just like ls. What you can see is what it can see, so it cannot count files that you cannot access.

You can tell it not to complain about files it cannot access by discarding stderr:

du -hLlxcs allysek 2>/dev/null

No. Compare the output of

du -shc /

vs

sudo du -shc /