If you use MG cross platform desktop project the dualshock controller should work.
MonoGame for Windows DX projects only uses XInput, not DirectInput which is an older lower level API that MS no longer recommends using for gamepads. But since dualshock gamepads do not support XInput they do not work with MG DX. In a DesktopGL (cross platform desktop) project MonoGame uses SDL for handling input. SDL can use DirectInput as well and has mappings for dualshock controllers so that should work.
We could look into supporting DirectInput with the mappings from SDL in DX projects as a fallback.
We could read just the windows part of the mapping file. I'm already messing around with SharpDX because we're updating it, so I could dig into this. And I have a dualshock controller to test with With DirectInput I think we could also support the Joystick API on WinDX.