Well, to answer that question first, no, Sophie Thatcher's character in The Book of Boba Fett is not the Dark Jedi known as Arden Lyn. According to Slash Film, Sophie is playing a character named Dratch, and she was the speeder bike woman that was in the series trailer. However, we can still theorize if Arden will appear in the highly anticipated Disney Plus series!
Arden is a Dark Jedi? Isn't that just a Sith?
Arden was born around the early days of the Old Republic (so basically the ruling government of the galaxy until the Empire took over in Revenge of the Sith). She was Force-sensitive, which means that Arden could be trained in the ways of the Jedi (to reiterate, this was the era before the Jedi were exterminated by Order 66).
According to the Star Wars Fandom Wiki, instead of following the traditional teachings of the Jedi Order, Arden pulled an Anakin Skywalker before it was cool. She fell in with a group of like-minded Jedi called the Legions of Lettow. In the group, embracing the Dark Side of the Force wasn't frowned on, but rather actively encouraged. Arden also learned the art of falling into a Force trance. This ability allowed the user to fall into a deep coma, so to speak, for years or decades without even aging.
Arden never technically became a Sith, but she did serve one for a while.
Emperor Palpatine seemed to favor the method of enticing new Dark Side employees with false promises of saving their loved ones (didn't work so well for Anakin though). Palpatine pulled this same manipulative maneuver with Arden, with a promise to resurrect her dead lover if she served him and the new Galactic Empire. Arden agrees to serve Palpatine, but she turns against him when she realizes he lied to her about basically everything.
Arden attempts to join a coup to take Palpatine down once and for all. Obviously, it doesn't work because Palpatine rules the galaxy until the events of Return of the Jedi. However, Arden's action demonstrated that even though she was technically a Dark Jedi, she was not on the side of the Sith by any means.
Arden is eventually murdered by Palpatine.
In the year 10 ABY (after the Battle of Yavin), Palpatine is resurrected as a clone. He enacts revenge against Arden by murdering her, as evil resurrected Sith Lords tend to do. However, given that The Mandalorian takes place in the year 9 ABY and the speculation that The Book of Boba Fett happens in the same year as The Mandalorian, it is still possible for Arden to make her first live-action appearance.
Arden is definitely a compelling Star Wars character, and it would be great to introduce more female Jedi into the world of The Book of Boba Fett. We don't know if Arden will appear in the series just yet. However, you can stream The Book of Boba Fett on Disney Plus on Dec. 29, 2021. New episodes drop Wednesdays.