I too am not sure if they'll reject an app simply because it wasn't built with Xcode, but there's also the code signing requirement. I highly doubt that any third-party IDE will be able to process the Apple-issued signing assets. If an app isn't signed by you when you submit it, of course it'll get rejected. You could try running the codesign command line tool to do it yourself, but again, I'm not sure that will work.
Besides, if you use a third-party IDE, you won't be able to use the Apple SDKs, which means that you'll likely miss out on everything special Apple hardware has to offer; on top of that, you wouldn't be able to have a truly cross-platform app anyway because iOS and Android are so fundamentally different.
Here's my recommendation: split your app into its core (the back end) and its UI (the front end). The core you can write using C++ or whatever suits your fancy; the UI you should write using the preferred IDE for each platform. On Xcode you can compile the core and iOS-specific UI into the iOS app, and on the other IDE you can take that same core and combine it with the Android-specific UI to create the Android app.