This is a sort of half answer.
As I understand it Deep Freeze has different versions for different operating systems - Windows, Mac and Linux - which I would take to mean that is only sees and protects the operating system on which it is installed - so, if on Windows, would not know that a dual-boot Linux system is there and so would not block it from making changes to itself.
It can also be installed inside a VMWare box so, presumably, if you ran your Linux system inside a VMPlayer and did not instal Deep Freeze there then, again, you would be free to do what you wished with Linux.
Maybe it's just me but I don't see the point in software which prevents you making permanent changes to anything unless you are simply wishing to test an operating system or software - both of which VMWare does well. I know that Deep Freeze allows something called 'thaw space' where changes can be stored for later - but what stops that infecting your computer if an infected file is downloaded?
If you do decide to proceed I and, I'm sure, many other Linux users would be interested i n how you get on.