at what stages may the supervisor be involved in during the
recuritment and selection process

This would depend on jurisdiction and company policy, but I cannot
think of why law would bar the supervisior from doing so right from
the start.

In the many companies, where I applied; as soon as the human resources
department determined that the applicant might be a valuable employee,
they arranged interviews with supervisors, department heads and/or
lead technicians in appropriate departments.
 Now that applicants frequently lie big time, human resources may spot
check parts of the application before envolving supervisors. Haste is
justified as the best candidates will be hired by someone else if
there is any significant delay. Small companies often have no human
resource person so the supervisors/owners review the applications and
schedule the interviews sometimes before even seeing the application.
In most companies lies on the application are sufficient reason for
termination.  Neil