We know it works for profession quests, what else might allow retroactive requirement rewards? My Hope is village specializations. This could come in handy with several options, warmonger and enchanter come to mind. Also if it takes a while for him to reach village level 2, this would allow him to build and upgrade a core library/ houseof knowledge/ University and utilize a professed librarian to get some serious research done now, then insta-level the technocrat specialization once he finally masters the catacombs.
It could depend on which one. If 20% of your population are fighters...that might work. But otherwise I don't think so. We can also see this in text. Dungeon level 1, Conditions for level 2: "Leveling Conditions: Generate 0/1,000 Dungeon Points" BK7 This would have been nearly a week after the Dungeon was created and gaining points. This is also seen in later leveling conditions.
"Leveling Conditions [2→3]: Generate 4,188/2,500 Dungeon Points Add a new Beast to the Dungeon Bestiary" Book 7 "Leveling Conditions [3→4]: Generate 4,188/5,000 Dungeon Points Add 0/3 new Beasts to the Dungeon Bestiary Add 0/1 new Rooms" book 7 From this we can also see that retroactive doesn't work. At this point in time there were three beast: pigs, dogs, chupacabra. Only the chupacabra counted for leveling the specialization from 2→3. This is because the pig and dog were before the specialization was selected.
Also another reason to take the tech specialization earlier, your only gonna research more tech, you're losing easy points by not including the base /cheap techs as well as the ones he gets for free from randy and other job holding citizens.
My bet it the benefits of the research center will be peanuts in comparison to the core library if he ends up going down that route paired with the tech specialization. It has to if he wants to keep up with every other op thing.