PHP releases avoid any type of syntax-breaking changes at the minor-version-release level, so as long as you're still PHP 5.5 your code will almost certainly still be valid. Since you have multiple servers, you could try upgrading one of them, completing your test suite/unit test/basic sanity tests/etc. first before rolling out the upgrade to all your servers.
You could spend a lot of time poring through the diffs on the commits referenced in that post, but ultimately you may find a move from 5.5.1 to 5.5.12 is fairly safe and may yield other improvements too, so I'd focus your energy on testing.