I use the same persistent Knoppix 7.2.0 version.
I have Eclipse and Java versions as follows:
Version: 3.8.0
Build id: I20120502-2000
And the following version of Java in my system:
java version "1.6.0_27"
OpenJDK Runtime Environment (IcedTea6 1.12.5) (6b27-1.12.5-1)
OpenJDK Client VM (build 20.0-b12, mixed mode, sharing)
I have downloaded, extracted the folder and copied the jdk1.8.0_144 folder to the /home/knoppix directory.

This link: JDK Installation for Linux Platforms could be perused, particularly, Installation of the 32-bit JDK on Linux Platforms
It is clearly mentioned that:
The archive binary can be installed by anyone (not only root users), in any location that you can write to. However, only the root user can install the JDK into the system location.

My query is: Will the installation by root be persistent? Or is it likely to be partly overwritten during subsequent booting?

If it is likely to be partly overwritten, I shall then proceed to install it from the /home/knoppix directory.