In New Jersey I think you need a firearm permit to be able to have a paintball gun. People often become felons for having items like that; be careful where you are.
If I were shot at with a paintball gun and thought I had been shot or shot at for real, which would not be an unreasonable assumption, I would defend myself with as much force as I could muster. If that meant running away, I would do that first, but if I felt I had no other choice, then the person with the fake gun would be shot at with a real gun. I would do whatever I could do to stop what I perceived as a lethal threat. I am going to do what I can to survive. Bad guys and good guys alike usually want to live and many will violently do what they can to achieve that goal.
I've been hit with paintballs and have shot others as well. One time there were 3 of us and we stood in a triangle about 20 feet from each other and unloaded on each other as fast as we could. We were laughing and whooping. You know that saying, "It's all fun a games until someone loses an eye?" I got shot in the face. It sucked. I had lost vision in my eye and wasn't feeling too good about that for a few minutes. I was fine after a rest. Getting hit with a paintball will get your attention. Body shots sting and even bruise with a thin shirt, but they will in no way that I can see disable a healthy person. If you are wearing a winter coat, there is no pain, and furthermore, there is no discomfort.
Most of the time criminals aren't looking for a fight and will run from the threat of lethal force. A faux gun will likely help you in those cases. But if you bumped up against a real bad guy, someone who had no qualms about stabbing or violating you, having a faux gun could easily be worse than having no gun of any kind. Threatening a bad guy with a toy when your life is at stake may prevent you from having enough time to utilize a more effective method of self defense (calling 911, running, using a real gun, driving away); in this case, a fake gun would be worse than nothing at all.
One other possible negative is if you escalate the situation with the threat of lethal force with a faux gun, the bad guy with a real gun may escalate with real lethal force and shoot at you, possibly striking people and property behind you. I'm not saying this to demonstrate the legal consequences of such an action. I'm saying this so you know that if you want to go down that road, you need to think about all the potential consequences of your actions/inactions. My point is I don't know of any method of self defense that doesn't have a down side; all the consequences, both positive and negative must be weighed.
Being the victim of a crime like this is very small, so statistically, you should be fine, but if you want to prepare for a truly bad deal, skip the fake crap and get capable. At least be prepared in case the fake stuff doesn't fool him/her/them/it.
Know that if you don't want to use lethal force, don't want to increase your situational awareness, don't want to get into the habit of locking your doors every time, etc., in defense of yourself that is fine. I'm all for using the least amount of force when reasonable, but I don't stop there. If the barking doesn't work, then the biting begins. What we do to defend ourselves is an individual choice. Just don't fool yourself into thinking that a paintball gun will provide more defense/safety than it can actually provide. I'm not saying don't use a paintball gun, just be aware of its capabilities and balance that with its limitations so you can better manage your risk.
Also be aware of the second time you may be victimized- the time you may spend in court defending yourself both legally and civilly. The choices you make now could have long term consequences. Yes, you want to make it out alive, preferably intact; however, you will likely want some semblance of the life you previously had before a violent encounter.