Will a car still start if the starter is wired wrong

"Wrong" is not something I can analyze. There is one small wire that bolts to the small terminal on the starter. It is impossible to put that one in the wrong place. The larger battery cable goes to the large terminal. You are not likely to get that one wrong either.

Where mistakes can be made is GM likes to use that larger terminal as a convenient tie point for other circuits. That is done simply to reduce the amount of wire needed for multiple circuits that run back to the battery. Sometimes those wire are overlooked and are not hooked up. One may feed the entire interior of the car, and one may come from the generator. If the first one is left off, everything inside the car, including the ignition switch, will be dead. If the second one is overlooked, the battery will run down in about a half hour of driving, then the engine will stall.

To verify the generator wire was left off, measure the battery voltage while the engine is running. It must be between 13.75 and 14.75 volts. If it stays around 12.6 volts or less, measure the voltage on the large output terminal on the back of the generator. If you find a higher voltage there than at the battery, that output wire is not making it back to the battery, and that indeed could be that forgotten wire by the starter.

Hi DJ1. You're thinking of much older starters with "S" and "R" terminals along with the large battery cable terminal. The "S" terminal is for the solenoid and gets 12 volts from the ignition switch or circuit. The "R" terminal, when it was used, is for a relay, meaning a switch that applied full battery voltage to the ignition system during cranking. Going back to breaker points, those systems used a resistor to limit current through the ignition coil to reduce overheating those points. The problem was battery voltage got drawn down during cranking, reducing the spark voltage and making the engine hard to start. Placing full battery voltage, now around 9.6 to 11.0 volts, on the ignition system brought spark voltage back up during cranking. Ford did that with a tap on their starter solenoids on the fender. Chrysler did that with a separate tap on the ignition switch. GM did that with their "R" terminal on the starter solenoid.

That dropping resistor in ignition systems isn't used on newer models, so there is nothing to bypass during cranking. As such, no second small terminal on the starter solenoid is needed. You can find some starters with the "R" terminal when it isn't used or needed as they were holdovers from previous years. GM redesigned their starters and generators for the 1987 model year and really ruined them. Their generators, in particular, went from the world's second-best design, in my opinion, to by far the worst design ever, with little inclination to improve it. The starters went to a permanent magnet, gear-reduction design. They have their own problems, but not nearly as bad as the generators.

When you do have an older starter with the two smaller terminals, it's true they are the same size, and the wires can be accidentally placed on the wrong studs. The starter will not crank that way because you're applying switched 12 volts to a terminal that doesn't go anywhere. 12 volts must be applied to the "S" terminal to activate the electromagnetic coil in the solenoid. That causes a plunger to move and push the starter's drive gear into engagement with the ring gear on the flex plate. Once that occurs, a contact disc makes the high-current electrical contact to send current to the starter motor.

To add a comment about those smaller studs, I ran into some that had a flat spot on one side, with a matching "D"-shaped hole in the terminal. I've heard that was done so the wrong wire couldn't be attached to one of those studs, but I suspect it was more likely done so the terminal wouldn't spin and twist wires as the nut was tightened. I don't remember if both studs had the flat side or if it was just one of them.