No, the heavy duty wire will connect to the solenoid, there will also be another wire going to this, this is the switched feed to the starter, I don't think there will be a relay.
The other wire from the battery will feed the whole electrical system, assuming it's OE.
If it were me I would disconnect the said wire from the starter (thinner one) disconnect battery before doing so, if it still starts then you have a problem with the solenoid.
Martin