That’s not how dedicated drops work in this game.
There are two separate loot pools for enemies with dedicated drops.
The Dedicated Drop pool is calculated first, before anything else. Dedicated loot is calculated even before things like your Mayhem levels are taken in to account. Going to a higher Mayhem setting does NOT improve your chances of getting a dedicated drop, nor based on my testing, does it have any measurable effect on your odds of that dedicated drop being anointed.
In short, Mayhem 1 and Mayhem 4 have the exact same odds of getting a dedicated drop, and for that dedicated drop to be anointed. As far as I can tell (Having done thousands of farming runs in this game) Luck modifiers (Artifacts, Guardian Rank) make no difference to Dedicated Drop items either.
Then, after the Dedicated Drop calculations are done, it moves on to the World Drop Pool.
World Drop items aren’t pure RNG. That’s obvious. Everyone here has probably received hundreds if not thousands of Woodblockers, ASDMs, Malek’s Bane, and The Lob while finding it much more difficult to get a Cutsman in comparison. But it’s world drop items where Luck modifiers, Mayhem levels, and all of that factors in to loot.
Now, as for this event, it only effects Dedicated Drop items as far as I know, and the notes don’t say anything about changing drop rates of major bosses, only rare spawns and Trial bosses, as well as the Maliwan Takedown. So I wouldn’t expect to see any difference at all unless you are farming one of those sources for a dedicated drop.
And if you’re doing that then you may as well farm at Mayhem 1 and make more runs faster than setting up a higher Mayhem level. With the exception of the Maliwan Mayhem 4 only drops, farming at M4 is just making it harder to farm with no benefit.