The short answer is yes. Barring any unusual circumstances, Pipedrive automations respond to the triggers that are set. If the trigger is a change in status, as you suggest, the programmed action will follow. Pipedrive triggers "do not know" how the status was changed... but when the status does change, the automation proceeds as programmed. Our Saas application (BrokrBindr, for mortgage brokers) is integrated to Pipedrive through webhooks. When our customers change a status in BrokrBindr, it also changes immediately in Pipedrive... and many of our customers have automations that then kick in (send email, create task, etc).
Hope this helps. Have a great week.