[Plugin: Search and Replace] Could we use this plugin to increase WP security?

No, not at all. And that would not increase security one bit, BUT would break your installation the next time an update comes out.

If you want to secure your installation don’t look to breaking (and making completely unsupportable) your WordPress installation. Instead follow some good proven advice.

https://codex.www.ads-software.com/Hardening_WordPress
https://www.studiopress.com/tips/wordpress-site-security.htm