Note that this response presumes Linux. I don't have enough experience with FreeBSD to write about it authoritatively.
Over the years it's been recommended to never accept an automatic kernel update because if the new kernel won't run on your server (for example if a driver required by your hardware isn't compatible) your system could be down and you might have to make a trip to the datacenter to fix it.
However, over time kernels have become well standardized, and if you're using a major Linux distribution (most of us are, on our DirectAdmin-based servers), and the standard kernel installed on your server without additional drivers, the updates will work. So you can remove kernel references from your exclude list
but at your own peril.
YUM kernel updates will install the new kernel, and will update the server startup scripts, generally either GRUB or LILO) (for an unerstanding of how linux boots, look
here [ibm.com]). The kernel itself won't run until/unless the server is rebooted, and if it won't start a datacenter trip may be necessary to edit the GRUB or LILO configuration if you don't have remote keyboard/monitor to your server.
Jeff