At what point does the database upgrade happen? If I unzip the downloaded magento image over my current installation, will that also upgrades database changes if any?
The upgrade happens the first time your magento application boots. Usually this is the first http request that gets to a magento page. So basically you just need to look at a page to trigger the database update.
An alternative approach is to use the handy magerun cli tool to trigger the updates:
I like this approach as it gives you full control over when the updates happen. You can put the site in maintenance mode so no traffic gets to magento and triggers the update when your not expecting, run the updates manually from your cli, test and then when your ready take the site out of maintenance.