The drukhari are slowly drained by Slaanesh in part because they've allowed their psychic defenses to atrophy.
Following Ynnead replaces one pull with another. Their soul is still consigned to a Warp entity (albeit one they chose), and is still drained over time, but when they die they join Ynnead instead of being consumed by She-Who-Thirsts.
I imagine the question of "which of the two of them is siphoning our souls on a nightly basis?" would be a lively debate if the drukhari were interested in debating it. Unfortunately, they probably aren't. The most knowledgeable about the process are the haemonculi, and they aren't sharing what they know, often not even with each other. The Commorrite loyalists of the kabals and cults are living in denial: they don't openly discuss their relationship with Slaanesh, treating their immortality and psychic vampirism as a natural facet of themselves. Those few who were pressed to the question would say Slaanesh is still eating the souls of the Ynnari, either out of fear of reprisal for saying otherwise, or because they refuse to believe otherwise out of fear. I imagine the Drukhari who joined Ynnead, possessed of a great deal of faith (they'd have to be, after all), would most likely believe that Ynnead is the one taking their essence now. There may be a small group of them who believes Slaanesh steals their psychic essence, and chooses to 'starve' themselves as long as they can in order to deny She-Who-Thirsts, but I imagine they're a very, very small number.