If Xehanort overrides her will with his own and uses her as a puppet she would not have a choice, much like it was intended for Sora.
In fact the only members who are known to be in Xehanort's new Organisation willingly are Ansem SoD, Xemnas, Young Xehanort and Xigbar.
Saix was implied by Nomura in the Ultimania to be the same as Xigbar, but there's still some controversy in the fandom if Saix is really, like Xigbar, an evil douchebag who sides willingly with Xehanort of if he's controlled against his will like Terra is.
That said, Xemnas originally sent those members considered traitors or "worthless" to Castle Oblivion in order to get rid of them, so Larxene being one of the darknesses would be rather slim, which however on the other hand would mean that Dilan (aka Xaldin) is a high possibility (he is still unstable according to Aeleus and he wasn't sent to Castle Oblivion, not to mention that as Xaldin he was quite the douchebag as well).
On this train, Luxord and ,sadly, even the useless twit Demyx are also candidates for being one of the 13 darknesses.