If you want to keep the computer safe, but avoid any other kinds of upgrades, you might fiddle with the repositories. You want to use the security repository, but none of the others.
The Security Repository:
from https://help.ubuntu.com/community/Repositories/Ubuntu/ , I quote:
[they are] designed to change the behavior of the package as little as possible -- in fact, the minimum required to resolve the security problem. As a result, they tend to be very low-risk to apply
How to use only the security repository
The usual way would be to change /etc/apt/sources.list to contain only the lines that refer to (ubuntu version name)-security.
This entails two problems:
* You would only get security upgrades even for chrome
* Ubuntu might overwrite the file from time to time, negating the configuration
To bypass that, you might want to take a look at this other answer
And how important is it to do this, anyway ?
No idea. Thought that was your question ...
I've had a desktop machine suffer attacks (as attempts to log into, via ssh) and it was kind of a trivial machine (nothing fancy in there to get peoples attention). That is all I know