I doubt very much it'd have a massive impact on the public personally. Sure, someone will no doubt realised they are the same ride model if it uses normal EF shuttles, but at the same time, I don't really see it have an enormous impact on SW7.
Both rides look set to offer a very different experience. Saw seems to focus mainly on it's theme and the drop. SW7 looks more dependant on inversions. Most people would no doubt look at SW7 and want to ride it purely because of the fact it "goes upside down loads". That alone is enough to sell the ride to most of the younger thrill seeking market.
It's like Nemesis Inferno being likened to Nemesis, not only for it's name, but no doubt the fact that it is an invered coaster that looks near enough identical with regards to train style and design. I shouldn't think it has too much affect on people, as both are different rides. If they were close then yes, there may be cause for concern.
But the GP are just like us, in the respect that they all like and look for different things in a ride. Some will ride something just because it inverts a good few times, others will ride something because it's fast or tall, and then there are some who will just ride anything because it's there. Regardless of if it's the same shuttles or not, there will always be plenty of people wanting to ride it, even if it is just once.
That's the way I see it anyway