Egwene thinks she can overcome the BEFORE she knows she's been dosed with forkroot!

KOD
Prologue

Abruptly it came to her that she was not shielded. Muddled she might be, but that made no sense at all. They could feel her strength, as she could theirs, and while none was weak, she thought she could overcome all five if she were quick enough. The True Source was a vast sun just beyond the edge of sight, calling to her. The first question was, did she dare try yet? In the state her head was, thought wading through knee-deep mud, whether she could actually embrace saidar was uncertain, and succeed or fail, they would know once she tried. Best to try recovering a little beforehand. The second question was, how long did she dare wait? They would not let her go unshielded forever.

Experimentally, she tried wiggling her toes inside her stout leather shoes, and was delighted when they moved obediently. Life seemed to be returning slowly to her arms and legs. She thought she might be able to raise her head now, if unsteadily. Whatever they had given her was wearing off. How long?

Events were taken out of her hands by the dark-haired sister sitting in the middle of the rear seat, who leaned forward and slapped her so hard that she toppled onto the lap of the woman she had been leaning against.

Her hand went to her stinging cheek on its own volition. So much for pretending unconsciousness.

“There was no need for that, Katerine,” a raspy voice said above her as its owner lifted her upright again. She could hold her head up, just, it turned out. Katerine. That would be Katerine Alruddin, a Red. It seemed important to identify her captors for some reason, though she knew nothing of Katerine beyond her name and Ajah. The sister she had fallen onto was yellow-haired, but her moon-shadowed face belonged to a stranger. “I think you gave her too much of the forkroot,” the woman went on.

A chill flashed through her. So that was what she had been fed! She racked her brain for everything Nynaeve had told her about that vile tea, but her thoughts were still slow. Better, though, it seemed. She was sure Nynaeve had said the effects took some time to go away completely.
“I gave her the exact dose, Felaana,” the sister who had slapped her replied dryly, “and as you can see, it is leaving her precisely as it should. I want her able to walk by the time we reach the Tower. I certainly don’t intend to help carry her again,” she finished with a glare for the sister seated to Egwene’s left, who shook her head, beaded braids clicking faintly. That was Pritalle Nerbaijan, a Yellow who had done her best to avoid teaching novices or Accepted and made little secret of her dislike for the task when forced to it.

Clearly the AS have been experimenting with the effects of forkroot and knew exactly how much to give her to prevent her from being able to Channel with any strength for hours, but to make sure she was awake within a certain time frame. Just as clearly she was given a pretty strong does as it knocked her out for a while... compare to what she has to say about this dose that did not knock her out...

TGS
In The White Tower

Three hours of working the kitchens did little to improve her mood. Laras, the hefty Mistress of Kitchens, had set Egwene at scrubbing out one of the oven like fireplaces. It was dirty, grimy work, not conducive to thinking. Not that there were many ways out of her situation.
...

She continued, scratching with her scrape at a blackened section of brick, dimly lit by the lantern she'd left burning in a corner inside the fireplace. She itched to use the One Power; but the Reds outside would sense her channeling, and she'd discovered that her afternoon dose of forkroot had been uncharacteristically strong, leaving her unable to channel as much as a trickle. In fact, it had been strong enough to leave her drowsy, which made the work even harder.

So she's given a dose not strong enough to knock her out, but she's still unable to channel even a trickle 3 hours later! It's no wonder no one is questioning Barasine alone holding the shield, and that's assuming they didn't go get another Sister if Katerine had been allowed to go!

In fact we know for fact that the effects of a strong does can keep her unable to Channel with any strength for most of the night ... we see it after she meets Verin! Just prior to that scene she takes a strong dose of forkroot (but not strong enough to even make her drowsy), and then proceeds to spend most of the night in study of Verin's book (by the time Meidani comes an entire candle has burned to a nub), and later when the Seanchan attack she can only barely grasp the source.

Silviana was being cautious indeed by having 2 strong sisters hold her shield while she slept.