Changing blower motors with different wiring schemes
On the wiring diagram the purple wire from the capacitor is shown completing a circuit with the black wire. 


No, that's not what the diagram says.  If they required you to jumper that, they would give instructions to that effect and the diagram would be clearer.  

The graphic is indicating which two wires are the LINE (supply) wires.  They are saying "This one is... and that one is". That's why the lines are dotted.