There is series of safety "interlocks" that must be closed/engaged before the controller will activate the solenoid.
Tow/Run on Run.
Key Switch ON.
FNR on Forward or Reverse.
Pedal microswitch closed.
MCOR Throttle signal more than 5% (not exactly sure on the minimum percentage).
With the pedal switch by-passed and all of the other interlocks ON, there is a small possibility of a signal fluctuation in the MCOR resistance track could cause the cart to move by itself.
It is very unlikely to cause it to move when you turn the key ON since too much pedal signal when the key is turned ON would trigger a HPD fault and the cart would not move.
So you should replace the MCOR, but that is how that switch plays in the entire safety system.
Edit:I am obviously not paying much attention this morning, You have a Series cart not a Sepex.
In this case the HPD fault would not protect you from a throttle signal issue accidentally causing movement at Key ON.
Make sure the key is always OFF when you are stopped and your foot is not on the brake if you use the cart with the by-pass in place.