The long answer is also yes, but please try it with the anchovies first. The thing about puttanesca sauce is that you really can't taste the anchovies. They melt into the sauce and just give it a mild umami flavor. It's subtle, like spaghetti with tomato sauce, but turned up a level!  If you do make this without the anchovies, you'll need to increase the salt a tiny bit. You can also serve this with Parmesan on top too and know that you're not breaking the cheese and fish rule. (Not that I have ever been one to pay attention to that rule.)