It's possible to overlay a newer kernel on top of a CentOS or RHEL installation. Reasons for doing so vary, but usually, there's a feature or kernel functionality that may be desirable. I wouldn't upgrade for the hell of it, though.
In my normal use case, I use a newer realtime kernels, either hand-compiled or as provided via RHEL's MRG distribution (or the free equivalents). That's a fairly specialized application, though.
For you, the drawbacks are compatibility, complexity and obviously, updates. It's slightly against the principle of using an Enterprise™ distribution.
The approach Red Hat takes for its enterprise operating systems is to create a consistent target throughout the support lifecycle of the OS. Larger corporations and enterprise applications need to guarantee binary compatibility throughout the 7 years that this OS platform is supported for. Red Hat will not change minor version numbers of a package (or kernel), but will instead back-port changes and security patches from newer versions into the older package. E.g., you'll never see Apache 2.2.23 in RHEL 5, but you'll see the relevant security patches (and some functionality) ported from newer versions of Apache into the 2.2.3. Same for kernel major/minor versions.
Upgrading the kernel outside of this ecosystem is a little risky, but can be done.