In answer to the question "Do ants harm or benefit peonies?", neither one, they are neutral. The collective wisdom of growers and gardeners seems to be that they arrive for the nectar and when the nectar is gone, they disappear.       

     ANTS ON MY PLANTS

• Peony plants-

• A ballroom fair,

•  

• The ants are dancing-

• In the air,

•  

• For nectar sweet-

• They climb the stair,

•  

•  They do no harm-

• While they are there,

•  

• It’s an annual ball-

• They waltz so sweetly,

•  

•  Then gorge on sugar-

• And vanish completely.

                                        -Karen Goodrich