No, he still has this wrong perception but he will never fall into the views related to Sakkaya ditthi.
In the Duthiya Isidatta sutta of the Samyutta Nikaya, it is stated that various other wrong views and the sixty-two wrong views described in the Brahmajala sutta arise due to the presence of sakkaya ditthi and that they do not arise when there is no sakkaya ditthi. The ten other wrong views described in the Duthiya Isidatta sutta are;
The world is eternal.
The world is not eternal.
The world is finite.
The world is not finite.
The soul and the body are the same.
The soul and the body are not the same.
One exists after death.
One does not exist after death.
One both exists and does not exist after death.
One neither exists nor does not exist after death (6).
I believe it is this aspect of Sakkaya ditthi that a sotāpanna has eliminated, right?