Not for the Appendix 2 test, which for this profession is satisfied by a baccalaureate degree. Whether she may lawfully practise once admitted is a separate question decided by state regulation and by her employer's requirements, and it can stop the job even when the immigration category is available.
Two permissions, and only one of them is an immigration question
Hypothetical example: Imelda is a Canadian citizen and a social worker at a Callander community mental-health agency. It is worth being precise about which rule does what. The listed profession here carries a degree requirement and no licensing condition, so Imelda's Bachelor of Social Work answers the credential half of the test directly.
The other half asks whether the American position is genuinely professional social work rather than administration or programme coordination wearing a professional title, and the described duties decide that. Neither half addresses state regulation of practice. Many states restrict who may deliver clinical social work services, use protected titles or bill certain payers, and an employer contracting with school districts will have its own insurance and accreditation requirements on top.
Those constraints do not make her ineligible for the category; they determine whether the job as described can lawfully be done. Establishing them early, in writing, is what keeps a valid admission from becoming a job she cannot start. Deciding at the outset who inside the American organization owns that question also saves weeks.