Hi jazzy_beat,
No, the status of the Freeze button cannot be saved in Registrations.
The purpose of the Freeze function is that the parameter group(s) previously set in the Freeze setting display (press "Direct Access > Freeze") can no longer be changed by Registrations, OTS or MIDI files. However, you can easily edit your registrations so that certain parameter groups are not changed when a registration is called up.
For example, if you don't want a particular registration to switch the current style, just re-memorize each registration button "back to itself", but with the Style box unticked (and at least with the Voice and Keyboard Harmony boxes ticked). Then re-save the bank.
Hope this helps!
Chris