Mask clip with transparency in DaVinci Resolve
Yes.  


Navigate to your .png in the media browser and import it into your project
Create a bin, make sure the new bin is selected.  Unfortunately, Resolve won't let you import the same image twice, regardless of which channels you're interpreting.  Using a second bin is a workaround.
Right-click on the .png again in the media browser, and select "add into media pool as a matte"

Drop the original .png onto your timeline above whatever footage you want to be the background
open the color page and select the fox.png clip in the timeline
right click on the background of the node editor and add an alpha output, wire the output of node 1 to the master alpha out.
right click on node 1, and from the context menu, choose your matte from the Add Matte submenu at the bottom

use any other roto tools you need to knock out whatever you need to knock out.