Is it possible to have the alarm sound in Max Power saving Mode?
I discovered the answer literally 1 minute after asking the question so I thought I'd answer it myself in case it's of any advantage to anyone else.

There's a very simple ( but quite odd in my opinion ) solution to this. Simply adding the clock app to the the shortcut screen of Max Power Saving Mode ( by clicking one of the plus signs ) solves the issue completely.

With the shortcut added - the alarm sounds. Without it - silence.