Starter Solenoid Rubber Plug

[barngal6]

I accidentally pulled out the starter solenoid rubber plug , where the little brown wire to the solenoid attaches.
I noticed the inside of the plug has a copper wire that was spiraled, at first I thought it was like that
but now I realize the copper wire probably attached to something inside and I broke it..
do I have to replace the starter?
What a hokey little piece, the solenoid wire was on tight so the plug just turned, initially...I don't think there is a nut to hold tje stid when you take off the solenoid wire..

When I reinstall the battery, will I be able to tell is I broke it just be turning the key before I turn it on?
I still have to purge the powersteering and replace some antifreeze, so I'd rather not try to start the truck till I have someone to help add the fluids...but I want to know if it is broken asap...