from my memory, no they dont. pick your poison and farm bronze medals now instead of Chaos talons, during the next batch instead of demon hearts or the last batch instead of reverse scales
on the last 1 or 1 and 1/2 days you get the 40AP version where you fight 7 servants and they all drop gold so you get 10-14 medals per run... but its not a lot of time to farm it without refils