In simplest terms, the answer to your question(s) is 'No'. However all of these depend on how integrated the PhVQA in your organization is. If PhVQA reports to the head of Global Safety, then he/she may expect that PhVQA is trained on all SOPs/WIs.
If PhVQA has an independent reporting, then it may not be necessary to be trained on the PhV SOPs/WIs unless the PhVQA is one of the reviewers of the PhV documents including SOPs/WIs.
All in all, it is ideal to have an embedded PhV system with PhVQA supporting the functions on a daily basis.