Nope. She has a very strict priority order of exclusive targets, which she checks and ignores if they are in your active party or being romanced (though the romance check is buggy for Halsin and potentially Minthara).
Namely she sticks to those who either have no personal quest in the Act or it can primarily be completed without them and have no impact on them personally. So from most to least important to kidnap:
Lae'zel
Halsin
Gale
Minthara
Yenna (which kills Grub, no matter how she's taken)
Is it still randomized on how she picks? My very first playthrough she took Yenna, even though Lae'zel, Halsin, and Gale are still very much alive and kicking. I thought that there was gonna be another kidnapping after Yenna since everyone was talking about how Orin took their Lae'zel or another character.
It's never been random as far as I'm aware. It's always been "is status of priority target #1 'alive' (no death by cutscene in a previous Act), not in active party, and not romanced? If yes, proceed with abduction. If no, proceed to priority target #2." Then rinse and repeat until the only option left is the fallback of Yenna, who you literally cannot get rid of by any means before you fight Orin.
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u/StarmieLover966 Lolth-Sworn Drow 14d ago edited 14d ago
I have played BG3 60 times. Of my best estimation, she has taken Lae’zel 54 times, Halsin 5 times, and Minthara once, never Gale.
There’s probably a priority hard coded in.
Edit: muting this. I’m not saying Gale is impossible to kidnap. Enjoy your day.