This is purely qualitative, not one bit quantitative
I would expect some small 'stabilizing' contribution but not nearly as much as the aerodynamic stabilizing effect of a more normal ('external') tube fin.
Reason: Tube fins generate stability the same way conventional fins do: they use the airflow moving over the surface to generate a force (roughly) perpendicular to the airflow when the fin is placed at a small angle of attack (that is, when the rocket's axis is tilted a few degrees). This works with conventional fins because they see the 'full' airflow velocity (ignoring boundary layer effects, forebody effects, etceteras for sake of simplifying this example).
When you bury tubes inside the contour as you have shown I expect you will get reduced airflow through those tubes. Most of the airflow will likely flow around the exterior of the transition and aft BT. I do not think your internal tube fins will be as aerodynamically effective as normal external tube fins.
My two cents.