Yes, you can use staging to test and push a new PHP version to your live environment, but it isn’t strictly necessary to push from staging to live to update your PHP version. Here’s a brief overview of how you would change the PHP version without pushing from staging to live:
Create a staging site.
Go to the staging site and change the PHP version on the staging site.
If everything is okay and working as expected on the staging site (be sure to test your site thoroughly), switch the PHP version on the live site.