Yes, when you make 3 pointers you typically win. For example, the Spurs were 11-3 this year when making 18+ 3s this season. One strategy in the modern NBA is to make it so that games where you make three is not a rare occurrence.
The Spurs only made 18+ threes 14 times this year.
Compare that to:
Boston: 45 times, 38-7
Cleveland: 25 times, 23-2
OKC: 20 times, 18-2
It's not necessary though... On the flip side, the Rockets only did it 7 times, when they went 5-2.
I think everyone generally agrees that the Spurs can get by with one non-shooter in the lineup. I agree that Fox is enough of a 3P threat (he's right on the borderline of SpursBills metric, which I think was 2.5 3PM/100 IIRC, but they can correct me if I am wrong). He's not a guy teams are going to leave open and dare to shoot, which is what we can't have. Where we disagree is that you just assume Castle will be a good enough shooter, but I want to see it first. I actually believe he will develop a respectable 3 point shot... but I want to see it first. 28.5% ain't gonna cut it, but I like his willingness to shoot.