Op ups are rare at the best of times (particularly domestically), however one would presume that QF would be looking at status first, then fare class (if that was the determining factor), probably in this order (Fully Flexible, Flexi Saver, Super Saver then red e-Deals).
Have been op'd up three times (that I can remember) on red-e-deals with Qantas.
BNE-SYD (twice) and MEL-ADL.
Various reasons including Cancellation of flights meaning Y overbooked, and for trim [Please, no jokes, there was only about 12 people on the plane and only one pax in J. I was asked to join them ]
I think there are always enough Plats/Gold/Silvers to upgrade if the need arises without having to look at fare basis. Now that might come into play if they have to decide between various ppl to op-up, but unsure.
I certainly would not recommend anybody pay a higher fare just to try to improve their chances for an operational upgrade. Save the money and every now and then spend that saving on a confirmed business class seat. You will get to sit up front more often than hoping for op-ups.
But when it comes to needing someone to op-up, I expect some agents do it based purely on status, some based on seat location (getting two or more together to accommodate a group) and some will consider fare type paid. I don't expect there is a fixed rule that says they only upgrade those on flexible fares. Agent discretion plays a huge part in the process.
all of my operational upgrades both domestic and international (about half a dozen) have occured when there have been flight delays with knock on effects to my flight.
domestically i have gone from economy to business and international op upgrades have been J to F.
last time i flew LAX - BNE it was a 3 class plane sold as two and there were spare seats in the F cabin. they asked people in the J cabin if they would like to come forward. it was on business class service though.