Yes. You can see a few examples of this in the books. Some potential spoilers hidden.
In The Shadow Rising (Ch 55), when Nynaeve was chasing Liandrian and Riana through the Panarch's Palace in Tanchico, she connects her ability to channel (i.e. her anger) with her ability to see the glow of saidar:
Saidar faded from her as she sped down corridors and across courtyards. Holding on to anger was difficult when she was increasingly uneasy for Elayne. ...
Once she saw Liandrian, with her pale honey braids, and Riana, with that white streak in her black hair, hurrying down a flight of broad marble stairs; she could not see the glow of saidar around them, but from the way servants cried out and leaped from their path, they were whipping a way clear for themselves with the Power. It made her glad she had not tried to cling to the Source herself; they would have picked her out of the throng in an instant by the glow ...
Later in the same chapter, as you observed, Nynaeve asks Elayne to use the Power to destroy the male a'dam, and watches her attempt:
Nynaeve could not see the glow of saidar, of course, but the intent way the girl stared at the vile objects told her she was channeling. The bracelets and necklace lay there. Elayne frowned; her stare became more intent. Abruptly she shook her head.
In The Fires of Heaven (Ch 17), Nynaeve watches Elayne walk a tightrope in Valan Luca's circus, and believes she was using the Power:
For a moment Elayne stood on the platform smoothing her dress. The platform looked much smaller, and higher, with her on it. Then, delicately holding her skirts up as if to keep them out of mud, she stepped out onto the narrow rope. She might as well have been walking across a street. In a way, Nynaeve knew, she was. She could not see the glow of saidar, but she knew that Elayne had woven a path between the two platforms, of Air, no doubt, turned hard as stone.
In Lord of Chaos (Ch 30), when Nynaeve is interrogated by Sheriam, Nynaeve is unable to see the glow of saidar until she becomes angry enough to channel:
"I remember, Aes Sedai," she said sullenly, tensing for another blow. It did not come, but she could see the glow of saidar around Sheriam now. That glow seemed threatening. ...
Finally Nynaeve understood. Finally everything came together. The Yellow sisters' presence. Sheriam and Myrelle believing, then not believing, threatening her, snapping at her. It was all apurpose, all to make her angry enough to work her Healing ...
Having broken her block, Nynaeve expects to be able to see the glow of saidar surrounding a woman who is channelling in ordinary circumstances, as shown below.
In Knife of Dreams (Ch 27):
"One of them is channelling," Nynaeve said, just loudly enough for him to hear, as she climbed down from her saddle. "I can't see anything, so she's masked her ability and inverted the weave – and I wonder how the Seanchan learned that! – but she's channelling."