Interesting problem:
I saw on the official Absolute site, that Linux is not listed, also the signs always involve an .exe running = windows. How does an .exe work with Ubuntu, Debian? Prbably only if wine is installed. Also found on other forums people agreeing, that it does not work with linux.
In an mail from 2007 Absolute seems to represent the philosophy that Linux is a minor operating system, thats why they do not support it:

"From: Miguel Guhlin [mailto:[email protected]]
Sent: Monday, January 22, 2007
To: John Livingston
Subject: Re: April 10th, 2006 article "Protecting Deleted Files" - reference to Computrace

John:
Thanks for bringing the updates in Absolute Software's product, CompuTrace, to my attention! If you like, I can post an update on the article itself (which one are you referring to since it's published in several places?), as well as share it in my blog (which gets lots of visitors). That should ensure the correct information gets out...will that help clear up any misconceptions?

That said, I would also like the opportunity to ask some follow-up questions to your email. Two questions come to mind that I would love to have you share your unique insights on; those questions include the following:

1) What if the hard drive is repartitioned, and users employ dual-boot scenario, one side running Linux and the other Windows? If running Linux, would CompuTrace still work? 

*After repartitioning Computrace will work when running in Windows.*

2) You mention Eraser wouldn't cause removal of CompuTrace. If CompuTrace is part of the bios, I imagine that it would not. However, if the machine is reformatted using a utility like Darik's Boot-n-Nuke, loaded with a new Operating System (e.g. Linux), then pressed into service, would Absolute Software be able to find the equipment? In other words, would it still work as advertised? 

*Well we support Windows and MAC OS 10+ so yes; we would work if rebooted into a Windows world, but not if the user boots into Linux.*"
( full artice: http://www.mguhlin.org/2008/10/computrace-revisited.html?_escaped_fragment_=#! )

**edit**

I have found an older article, where it seems, that they listed ubuntu and debian as compatible, but the site is defunct. Also here the author says it does not disappear with reflashing.
Some other articles say, it is on a CHIP. Obviously there are different nformations from different times and versions.
Even if it shows "not activated", it does not mean, that computrace is not running and phoning home.

https://bartblaze.blogspot.de/2014/11/thoughts-on-absolute-computrace.html
 
I do not know yet, what is a real solution to this, it looks, like a permanent backdoor, which can be activated even if the customer had deactivated it.