This is absolutely not true for Linux kernel updating. While you won't be using the new kernel before rebooting, there's 0 risk in not rebooting, because there's exactly 1 version of the kernel running on the machine -- it's loaded into memory when your computer starts.
There's of course rare exceptions, like when a dynamically linked library you just installed depends on a minimum specific version of the Linux kernel you also just installed, but this is extremely rare in Linux land, as backwards compatibility of programs with older kernels is generally a given. "We do not break userspace"