does iTunes Match update play counts?

After a song has been uploaded to icloud and then downloaded to your computer, does it continue to update and store your play counts from there on out? I was listening to an album while adding new music and after I matched them I continued to listen to a few more songs and then exited iTunes. After opening it back up later I noticed the last few songs I listened to didn't save the play count. So I tested this out and listened to a few songs and then manually updated iTunes Match. I exited out and went back in and the play counts were up to date. Does this mean the play counts are updated in the cloud? If I were to load my account on another computer, would the play counts be synched?