If it's something she could realistically have learned while traveling Pharloom, or put together from listening to others conversations, then probably.
Shakra's learning about Hallownest in real time; at present (Chapter 9), she knows that there was a terrible plague a very long time ago, which significantly affected both Hornet and Hollow. She knows Hollow is a god or demigod, based on their relation to Hornet and Lace's confrontation with them in Chapter 6, but cares very little for the affairs of gods. That aside, she's just slowly increasing her knowledge the way she always does: interacting with the locals and mapping the region. (Normally combat is a way she learns, but the Gardens are very peaceful these days.)
She probably saw the Green Prince in Sinner's Road, but even if she stopped to talk with him, but even if she'd talked to him there, she'd either have respected his desire to be left alone or be put off by his passivity altogether. She never would have learned of Verdania's existence, and based on her maps, never found her way into their ruins; however, she did listen to Lace taunting the Green Prince in Chapter 2, and she's familiar with both the Citadel's expansion and the Haunting.
So she's reasonably concluded that the Green Prince (based on his title) is the leader of a tribe that was destroyed by the Citadel, that he lost his partner in the process, and that he's struggling with survivor's guilt (though nobody present would use that specific term). She can tell by the way he moves (and his brief scuffle with Lace) that he has combat training.
However, she doesn't know about his age, the specifics of Verdania's destruction, or anything related to the Cogwork Dancers. She doesn't know why he wears the Pristine Core, but can tell that it's emotionally significant to him.
She has much less context on Lace, but in their limited time together she's observed both Lace's emotional turmoil and physical frailty. She can tell from the way Lace holds herself and her pin that she's a trained, skilled combatant. She did genuinely assume her to be a child until she was corrected in Chapter 8. That said, even if she acknowledges that Lace is older than her, that doesn't translate to respecting her seniority lmao...
Anyways, most of the details of Lace's life wouldn't matter to her or change her behavior towards her (i.e. that she's significantly older, and an artificial being created directly by a pale god). There's other aspects of Lace's backstory that she might be sympathetic to, though, but that's something that we'll be covering in-comic.
