Do kernel updates require every version in between?

Ubuntu will only download and install the most recent kernel

I have an Ubuntu computer that stays turned off for months. When I turn it on and let it update itself, it only downloads the latests kernel, and skips the ones in between.

You may want to run

sudo apt autoremove

After each updating kernels so that /boot has only two most recently installed kernels. This way, if the latest kernel misbehaves you can go back to the previously working kernel, and at the same time keep /boot from getting clogged up with old kernels.

Hope this helps

Short answer: No

Longer answer: I have some Ubuntu flavour systems (Lubuntu and Xubuntu), that I run rather seldom. When I update & upgrade them, they will often skip several kernel versions, and there are no problems. I usually run the following commands, and receive the current kernel version (of the same kernel series),

sudo apt update
sudo apt full-upgrade

It is a good idea to run

sudo apt autoremove

after a new kernel is installed, so that /boot has only two most recently installed kernels. You can select the previous kernel from the grub menu, if there are problems with the new kernel.

Pinning is usually used only when you have mixed repositories

See https://help.ubuntu.com/community/PinningHowto

I suggest you put the kernel on hold

How to prevent updating of a specific package?

Either way, once you reverse the hold or pinning, apt will only download and update the most recent kernel skipping any and all kernels between.