Yes, it does.
CoM took place directly after KHI, and ended a year before KHII (when Sora slept for a year).
Although it isn't neccessary to play CoM, it does help people understand the story better. Little things like the "Thank Namine" written in Jiminy's journal, are all explained in CoM.
It also gives us a more in-depth look at the Organization, when they were all alive.
If anyone is interested, I suggest watching
these videos (for all people who haven't played CoM).
They show the important parts of CoM's story. It saves people from having to play the game.
(There's 20 videos, by the way. I only linked to the first one.)