I wouldn't say it counts as a postdoc, but I'm not aware of any state that explicitly requires a postdoc; rather, they require a certain amount of time of supervised clinical practice and the completion of a form afterward (and sometimes before) by the person who supervised you broadly describing what types of stuff you did while supervised.
But speaking to what ExecutiveDysfunction noted about independent vs. non-independent practice, you'll probably want to try to find a way to explicitly identify and track the cases on which you're receiving supervision (e.g., via a written supervision agreement, which some states actually require; co-signatures on your notes/reports; etc.).
Yes, so for example I am looking at CA's requirements for postdoctoral experience and the state lists the following criteria for postdoctoral work. If I ever for-see the need to move to CA or another state that requires postdoctoral hours, I would pursue getting a supervisor who could supervise me in an informal manner part time in order to accrue these hours.
(2) Postdoctoral SPE: At least 1500 hours of SPE shall be accrued postdoctorally. “Postdoctorally” means after the date certified as “meeting all the requirements for the doctoral degree” by the Registrar or Dean of the educational institution, or by the Director of Training of the doctoral program. Postdoctoral SPE may be accrued only as follows:
(A) For postdoctoral SPE accrued on or after January 1, 2006, in a formal postdoctoral training program pursuant to section 2911 of the code, which is accredited by the American Psychological Association (APA), or which is a member of the Association of Psychology Postdoctoral and Internship Centers (APPIC) or the California Psychology Internship Council (CAPIC) and registration with the board is not required; or
(B) As a registered psychologist pursuant to section 2909(d) of the code and registration with the board prior to commencing work is required; or
(C) As an employee of an exempt setting pursuant to section 2910 of the code and registration with the board is not required; or
(D) As a psychological assistant pursuant to section 2913 of the code and registration with the board prior to commencing work is required; or
(E) Pursuant to a Department of Mental Health Waiver (5751.2 Welfare and Institutions Code) for which registration with the board is not required.
(b) Supervision Requirements:
(1) Primary supervisors shall meet the requirements set forth in section 1387.1.
(2) Delegated supervisors shall meet the requirements set forth in section 1387.2.
(3) Trainees shall have no proprietary interest in the business of the primary or delegated supervisor(s) and shall not serve in any capacity which would hold influence over the primary or delegated supervisor(s)' judgment in providing supervision.
(4) Trainees shall be provided with supervision for 10% of the total time worked each week. At least one hour per week shall be face-to-face, direct, individual supervision with the primary supervisor.
(5) A maximum of forty four (44) hours per week will be credited toward meeting the SPE requirement. This shall include the required 10% supervision.
(6) The primary supervisor shall be employed by the same work setting as the trainee and be available to the trainee 100% of the time the trainee is accruing SPE. This availability may be in-person, by telephone, by pager or by other appropriate technology.
(7) Primary supervisors shall ensure that a plan is in place to protect the patient/client in the event a patient/client crisis or emergency occurs during any time the supervisor is not physically present at the established site at which the trainee is working. The primary supervisor shall ensure that the trainee thoroughly understands the plan in the event of a crisis/emergency.
(8) SPE shall not be obtained from supervisors who have received payment, monetary or otherwise, from the trainee for the purpose of providing such supervision.
(9) SPE gained while the trainee is functioning under another mental health license shall not be credited toward meeting the requirements for the psychologist's license.
(10) Prior to the start of the experience, the primary supervisor and the supervisee shall together prepare an agreement that outlines the structure and sequence of the planned program of supervision to accomplish the goals and objectives of the experience. Hours accrued prior to preparing such an agreement results in those hours not counting toward the licensure requirements.