Will this work to make my dog better?

I have a retired racing greyhound, he is a male, about 85 pounds, and he is absolutly beautiful and very sweet, very healthy and very loved. He used to be a little territorial towards people coming in the house, he would keep his distance and just bark. But ever since we had to put our cat down, he barks, growls, snaps, and tries to bite and even attack anybody who comes in, even if he sees them walking down the street. It's nothing medical, because in public he is perfectly fine with people and other dogs, and there are certain people he likes, and certain ones he doesn't. Fear aggression is also common in greyhounds I've learned. he's not mean, he's really a big baby! He's scared of loud noises and cries at things, and he walks on top of us so we can rub his belly, he's just trying to pretect us, and he doesn't know he's being "bad" I am 14 by the way, and we've been having my friend come over every thursday for a few hours to work with him. we give him chicken as she walks in and have her throw her some, and we kept him on a leash. it worked out well! He still gets shocked when she gets up from sitting somewhere. By this we are teaching him that people being welcomed in the house are not threats, they are friends. He's been doing quite well too. Now what we did a few days ago was we put up two gates in our house, so he was in one half of the house, and my friend and me were on the other side of the gate, that way he could be off the leash, and see my friend walking around, talking, and it worked amazingly! we sat next to gate and talked to him, and each other, she threw some treats over, she gave him a bone, and it was great. a few times he stuck his head over and barked, so we just acted like we were playing, we said "awww whataya doin cutie!" and just petted him, and it seemed to calm him down. so my question is, will this gate thing work? cus we dont like having him on a leash everytime, he needs more freedom you know? thanks!