WordPress has been updated! Before we send you on your way, we have to update your database to the newest version

This is a common message where the WP update also requires to make changes to the database.

The answer if this will cause problems or not is hard to give, but the solution is to test this on a staging or local development version of your site, which is not valuable.

Or, to make sure you have a very recent backup which you can easily revert to, in case you can only make this update on the production version.