This depends largely on what code you push exactly. The more custom the code, the more likely something may break at all. I've seen a lot of sites running similar commands as part of their deployment routine without a problem. Most likely it's drush cc all
that may abort due to memory limit exhaustion. But this won't break your site.
To ensure your commands will run successfully in your live environment I'd recommend to implement some sort of continuous integration. For example CircleCI (1.500 build minutes free per month) or TravisCI (free for open source projects). Here is an example: https://github.com/leymannx/drupal-circleci-behat. Though it's for Drupal 8 I guess you'll get the idea.
By that you'll basically set up your site from scratch inside some temporary and configurable server (Docker), import a dummy database, run your commands, maybe run some testing (Behat) and then ONLY when everything went fine the site will be deployed to the live server where your deployment commands run again.