No, the core_enrol_edit_user_enrolment is not for change user role in the enrolled course.
For assigning the role to a user you can use core_role_assign_roles.
What do you mean by changing the user role? Is it mean to unassign the current role of the user in that course and assign the new role?
Well as far in my knowledge there is no direct web service for this(unassign present role and assign new). You can do it in two steps:-
1) use core_role_unassign_roles to unassign current role.
2) use core_role_assign_roles to assign new role.
If you don't want to use these web service you can make your own web service for this functionality.
Regards
Mayank