I am using Magento CE 18.104.22.168 which ships with Zend Framework 1.12.3. Is it possible or a recommend practice to upgrade Zend Framework without upgrading the Magento version? Will upgrading Zend Framework to 1.12.19 from 1.12.3 break Magento core?
It's not a good practice to upgrade Zend Framework instead of Magento. Magento as platform is very dependent on the set of Zend Framework components and each Magento version addresses specific vulnerabilities from each Zend Framework version (there are even specific Magento patches for ZF).
I'd suggest you to keep Magento updated on its latest version, as well as keeping all the 3rd-party extensions updated.