Upgrading the kernel could
break the grub loader for that OS, and, in limited circumstances, for another Linux OS in a multi-boot set up, but only if a set of conditions existed, those being:
- That the kernel upgrade removed the old kernel and changed the name of the kernel image in /boot
- That the kernel upgrade over-writes a kernel belonging to a different OS
Personally, whilst I have seen the first, a simple sudo update-grub would fix it. I have never seen the second. If you are multi-booting including Windows, your Windows boot entry shouldn't be affected at all.
A fix should be relatively easy, by booting a live CD, chroot into the OS owning grub and sudo update-grub. Alternatively, you could boot a live CD, mount /boot and manually fix /boot/grub/grub.cfg