Not sure if I understand your question exactly, but the user will not be allowed to prune backup snapshots. So if you use the retention settings on the backup jobs in PVE (using the corresponding user for connection to the PBS), then no, the retention will not work as the user will need prune privileges to remove older snapshots. If you however let the PBS manage the pruning via dedicated prune jobs, then yes, the last 3 snapshots will be retained, pruning older ones.