It’s entirely possible. We don’t even know when they left though. Did they leave because they rejected Surak and either were forced off or voluntarily left because fuck that noise? Did they leave before that but after the nuclear war or wars? Did they leave even before that?

And if they did leave because they rejected Surak, was it immediate or was it an anti-Surak movement that grew over time?

We just don’t have enough information. Especially not considering it was so long ago that Vulcans forgot that the whole event even happened.