and I might crash these applications
1) One of the main reasons for using a well established distro - and particularly Centos (as essentially a copy of RHEL - a snapshot rather than a rolling release) is that any updates will retain backward compatability - the updates are unlikely break anything
2) If bits of code stored on disk are replaced with something which is incompatible, then there shouldn't be any impact until you try to load and run the new code - very few bits of software will perform any dynamic linking deferred after start up - hence the programs might not restart, but it's highly improbable that they will crash.
3) If there is any possibility of these systems being accessed remotely (or even locally with any possibility of malicious intent) you*must* keep your patches up to date.
4) in the case of kernel patches you must reboot the machine after applying the patch - i.e. your currently running code is going to be stopped
5) if you've got "lots of machines" and they are doing anything of value then you should have the capacity to test the updates on a non-mission critical system yourself (as vonbrand points out, you don't even need a dedicated machine for this).