Tim:
Although you can update a kernel, it's usually a bad idea.
Res:
generally, you should install new kernel, reboot, if no problems with a day remove old kernel
I would keep them longer than that. You might not thoroughly test a kernel within just a day or so. And an update to something else, afterwards, might present a problem between it and the new kernel. I think it's always best to keep at least one or two prior kernels.