Yes, you can!
From your Printful Dashboard, go to Stores → Your Etsy Store → Settings → Orders. Scroll down and make sure the “Import personalized orders as drafts” box is checked.
Then, on your Etsy store, go to Shop Manager → Listing and pick the listing you want to personalize. Click on the “personalization” tab and enter guidelines for your customers.
Whenever you receive an order with a product for personalization, it'll appear on your Printful Dashboard with a blue icon. Open the order, and hover over the icon. Here, you'll see the personalization request left by your customer.
To complete the order click the button right here and then “edit” and adjust the product to your customer's wishes, then follow the steps of manually confirming the order.
You can also watch this video tutorial on how to set up Printful + Etsy Personalization: