No in the sense that setup, draw, and event handlers are part of the Processing loop. Draw is called and then events are processed, then draw is called again. You can’t put draw in a class, although you could choose to invoke redraw(). Your code puts event handlers in a class, but you then still need to pass the events from keyPressed() to the Objects of that class – for example, looping over an array in keyPressed and passing each event to each object.
OR you could use registerMethod("keyEvent") – for a previous discussion, see:
Capturing keyEvent in own class: registerMethod() - Processing 2.x and 3.x Forum