Is it in theory possible to boot a Live CD on a Linode, such as a Slackware Live CD?

Yes, you can definitely create a Live CD disk. A lot of this information is similar to our Installing A Custom Distribution Guide, which you can find below. This can be done for any Distros Live CD, so if you wanted to boot off the Arch Live CD, simply find the download mirror and swap that in the DD command later.

Step One: Preparing the Disk and Configuration Profile.

Log into manager.linode.com , and navigate to the Linode that you wish to create the Live CD

Make sure that you have an adequate amount of space to make a Live CD disk, which may require shrinking your current disk. We have a great guide on how to resize a Linode Disk.

In this case, Slackwares most recent Live CD is 2.6 gigabytes worth of space, so we will want to create a 3000MB disk. I recommend naming the disk "Installer".

Also create a configuration profile with the following settings:
Kernel: Direct Disk
/dev/sda: Installer disk.
root / boot device: Standard /dev/sda

If you wish to add additional disks to your configuration, feel free, but make sure that the Installer disks and root/boot device is the same disk.

Step Two: Booting into Rescue mode, and creating the Live CD.

You will need to boot into Rescue mode in order to create your Live CD image. You can do this via the rescue tab in the Linode manager. You can also refer to our Rescue Mode guide for reference.

Next, you will need to run the following command, which will download then copy the Live CD to our Installer disk, /dev/sda:

curl https://mirrors.slackware.com/slackware/slackware-iso/slackware64-14.2-iso/slackware64-14.2-install-dvd.iso | dd of=/dev/sda

Once that curl and dd is done, power off the Linode and reboot into your installer profile. You will need to open up Glish, which you can find on the remote access tab in Linode Manager. You should now be booted into your Slackware Live CD!