It seems possible see this site where they are using a tool called PhoneGap build.
Yes, it is possible to build one. Yes, you do need a Mac for it, as far as I can tell. Although, this is interesting as well. You still need Apple id's en stuff, but it might be that you just need that and can rely on the Phonegap Build environment to build new your new releases.
On the other had, my experience is that you need an Apple environment to debug your app. At least at the beginning. When you've figured out how to use Phonegap for iOS, you might not need that anymore. Actually, the Phonegap application is just a wrapper, right?
Furthermore, there might be some issues with iOS apps. I started a thread on that.
Why do you need a native app? I've done the works to prove for myself that it works. And I wanted to use the camera, something you might be able to do with HTML5 on iOS6 but not on Android at the moment. But if I don't need to, I think it is always the best option to stick to the browser. I'm curious about your use case ...