I’ve had zcash update along with other installed software before during automatically scheduled updates. If you’ve already gone through the Debian binary package install process before, the only part of it you need to do to trigger an update to a specific new version is ‘sudo apt-get install zcash’ https://github.com/zcash/zcash/wiki/Debian-binary-packages
re: Your question, yes, you can use the update manager. This isn’t necessary but I like to stop zcashd if it’s running before doing such an update. Also, before an update and while zcashd isn’t running, it is also a good time to create a backup of the .zcash folder and all its contents if you’re in that particular habit.