No, it really doesnt happen like that. I didnt use parelli, but my mare will follow me anywhere with or without a halter, my girl was scared of going though water, her 'safe spot' is when I take her halter off and put the bridless/halterless rope on, so I did just that, and wwe jsut walked right through the water, we can gallop through water now, and her just trusting me to get her through that one thing.....she will do anything for me the first tiem I ask.
Just like what flitterbug said. Don't let that carrot stick leave your side. What I find useful is to let them loose in the arena (or round pen) and stand in the middle,with the thing they are scared of. 90% of the time they will eventually come to you, because if you do some groundwork before this with them then you are their 'safe spot' and they want to be near you. Im not sure if this will work with a horse that was beatin with it....... but maybe its worth a try?
But remember, Parelli DOES NOT work wih every horse, and if you are stubborn o stay with parelli...then get a different horse. Because it might not work with your horse, parelli might be the most advertised, but he is definily not the most knowing. You can choose whatever training technique works, but it is important that you desensitize your horse to the whip, show him he can relax and its not a bad thing