Linux headers is a set of low-level headers mostly used by toolchain packages, boot loaders and linux-specific tools.
The best test is to make sure gcc and glibc can survive rebuild and system reboot.
Also check if applications can still be built against newer headers. The list of tools known to use linux-headers directly is in testing HOWTO
new linux-headers / old linux kernel
It is fine to have new linux-headers (for example, 4.14) installed and old kernel running (for example, 3.13).
Software should accomodate (glibc does) for lack of runtime support of new syscalls, ioctls and such.
See kernel documentation for caveats and promises.
old linux-headers / new linux kernel
TODO: clarify in glibc upstream.
Despite the glibc FAQ entry it is fine to have old linux-headers (for example, 3.13) installed and new kernel running (for example, 4.14).
Userspace software will not be aware of new features (syscalls, ioctls, structs) added since 3.13 but it should not break things. Unless bugs in the software (should be fixed). Or found out why software breaks and this section should be fixed :)
linux-headers / linux kernel keywording policies
There is no direct relation of linux kernel versus linux-headers stabilization.
linux-headers are fine to be stabled as soon as they are ready and are known not to break userspace.