It depends on what circuits are sending power to the score motor. If those circuits are part of the playfield or backbox, then yes, it would stop the score motor from running when the Jones plugs get disconnected. But, this is a very difficult way to troubleshoot a continuously running score motor. It's much easier and quicker to pinpoint the issue with a schematic...

You'll need to look on your schematic to find the stuck switch that is causing the score motor to keep running. Find the score motor symbol on the schematic and work your way back through the switches so you can check/clean/adjust them. Of course, if one of the switches in the score motor circuit is located on the playfield, backbox and/or coin door that you unplugged, you wouldn't have to check those switches... Power off the machine while you're checking the switches. After the adjustments, power on the machine and see what happens...

That's a switch stack from a relay and it will need to be put back together before you start doing troubleshooting on the machine. Just look at the other relays that are installed on the main board and you should see how it goes back together...

Make sure there are credits on the credit unit. Clean and adjust all the contacts on the credit unit. Check the voltage at the start button switch with a test light or multi-meter. If there is no voltage at the start button switch, you'll need to find the start button switch on the schematic and trace back away from the coil symbols and go back through the switches to the transformer...

Switches throughout the machine should send power to the score motor until the machine is completely reset.

Check the switches with the "yellow/red" wire on these relays:

D, E, G, O, P, S, W (might be M), AX

And check score motor switch 1C with the yellow/red wire...