Device management is like the guy with the broom at the end of the parade - it will clean up specific out-of-date software on your computer, if someone else doesn't (e.g. you or auto update).
Device management does deploy updates to Chrome. This is intended, but not working reliably at the moment. When it works, it will happen irrespective of any 'dont update' setting done by a user or administrator.
Currently, the frequency of Chrome updates is causing older updates to be deactivated, usually, but not always before they can be applied. Our conservative and sequential "test hardy group1, then test diverse group2, then patch everyone" (Dogfood, Canary, Pandemic) patch cycle, often means no update can be applied, because a new one is available deactivating the old one before it makes it through the test cycle.
Fixing this problem is even harder than understanding my paragraph above, but the Device Management Core Team is working on it. Meanwhile, if you or your administrator has put your Chrome into "don't auto update" mode - stop that! :)
Device Management is merrily patching other software. Check back Aug 15 for our July statistics.