The good news is: Yes KiCad can work with pads shaped like your sketch. The bad news: There is no easy way to create them from within KiCad.
If you need that hard corner then you will need to use a polygon as the custom pad primitive. (meaning you will need to approximate the arch with line segments) There is no way to tell KiCad to do this approximation for you. (Meaning drawing by hand. Not really feasible.) Best option is to use freecad to generate such a pad for you: Kicad StepUp: The Sketcher for Footprint generation
If you can live with a rounded corner then you can use arcs and lines as primitives. For that draw your arcs and lines (overlapping by at least 0.1mm) on any layer using the normal graphical tools of kicad. Add a circular pad somewhere inside that area. Select the pad and all your graphical primitives -> right click -> make pad from selected shapes. (or similar wording i work from memory here)