None, or fragments at best.
In theory, up until the core sentient is plugged into a piece of Shadow technology, like one of their ships, recovery is still possible. We see that with Bester's love in Ship of Tears. The wetware plugged into her brain is feeding her instructions, and she's compelled, but there's clearly still a (highly traumatized) person behind all that.
Once plugged in, for lack of better terminology, the personality of the "ship" takes over, and it doesn't take very long at all for that to be all that's left. Passages are woven through The Passing of the Techno-Mages trilogy describing Anna as a ship, and her later extraction. For the record, Anna was part of the attack on the Narn in Quadrant 37, and her thoughts are little more than glee of the hunt, screaming at the thrill of combat.
She spun, crying out victory at her first kill. Together they fell upon the Narn ships, their mouths screaming destruction, their bodies cutting through the invigorating vacuum, swirling in a dizzying dance of death. Soon the Narn ships and the probe were in pieces, and Anna and her sister rejoiced in their power. The Eye showed Anna what she must do next: the outpost below, covered in flames, every building destroyed.
The only time Anna is ever shown the slightest piece of humanity is a brief hesitation during that battle.
One of the fighter's beams passed across her underside, its touch a brief, startling caress. Anna's war shriek stilled. Her body, which she had almost forgotten, lay at the heart of the machine, cold, longing for touch. She wanted to turn back, to feel the beam's caress again.
The march of the machine's beat stumbled...
She even has frustration at being assigned to non-combat roles; she spends a fair portion of the second book ferrying around a team of traitor mages and resenting it. Anna is later shot down by Galen, the main protagonist of the series, but survives and spends most of her time outside the ship mindlessly trying to merge with any computer system, including room controls and Galen himself. Of course, her wetware implants are still intact, so this is expected, but there's no trace of Anna fighting back at this point, like there was with Bester's love.
Anna does get put in a new Shadow ship but doesn't get much time in it before she's recognized and her confusion begins again. She is recalled to Z'ha'dum and they begin trying to prompt her old life to resurface even before they pull her out.
"Who are you?" the human named Justin asked. "What is your name? Your full name, Anna."
My name is Anna, she transmitted to him.
"Anna is part of your name. What is the rest?"
"Where were you born?" he asked.
I don't understand.
"Where are you from?"
There was nothing before Z'ha'dum.
"What are you, Anna?"
The man was an idiot. An engine of chaos and destruction.
"Before you joined with the ship, what were you? Who was Anna Sheridan?"
Sheridan. Now that he had said the word, she recalled it. But she didn't understand why she had a second name.
Even under orders from the Eye (the psychic presence that guards Z'ha'dum and acts as their own C&C), she resists being extracted (at least two techs die), and attempts to merge with the Eye itself. Once finally removed from her implants her thoughts remain shaped as though she still considers herself a ship. She has zero memory of her parents or of John Sheridan when prompted with photos. A telepath is brought in (whom Anna instinctively hates) and attempts to recover her memories, but the mental block created by Anna's conditioning is so strong that the effort to remove it would be way beyond lethal; it's far stronger than any mind-wipe.
There are further efforts, but most fail. Anna is given a chemical to break down her mental barriers, and starts remembering transitory images of her old life, but has zero connection to them. She's introduced to Morden and this has the only connection she ever grasps, as she remembers the tunnel they were in when they encountered the Shadows for the first time. That's it, nothing else. She has to be fed information on the life of the original Anna so that she can fake successfully, and retrained in how humans think and behave, along with playacting sessions so she could anticipate John's reactions and continue to persuade him. This appeared to take two months (the section is marked November 2260), and was not something that could simply be imprinted back onto her. In fact, her main motivation was that she could merge again, and they encouraged her cooperation with false promises that she would be part of the Eye soon. Her last act, screaming at the descending bomb, is treated like a regression, trying to scream defiance the same way the ships scream in space.
There might be some wiggle room. Other parts of that novel trilogy show other sentients in different pieces of Shadow tech (the one in the Eye, in fact) that seem to retain some minimal parts of their personality - but these are special pieces, whose conscription was not nearly as unwilling as Anna's.