Running Wordpress updates while in production?

Running Wordpress updates while in production?

We have a production site powered by Wordpress. In my experience,
Wordpress updates tend to go pretty smoothly, but every now an then
something goes wrong and so we always run the updates locally or on our
dev site first to make sure nothing breaks.
My questions is this: Is it a good practice to commit those changes (from
the upgrade) locally and then push the changes to production?
...effectively updating the production site? This seems to work, but I
know that sometimes updates include modifications to the database. So my
fear is that the update will modify my local DB, but NOT the production DB
and then cause problems when the newer code runs (expecting the DB to have
been modified).
Is this is valid concern?
Will well-written plugins account for this issue somehow?
Is there an entirely different and better way to do this?