It will not run x-code. You need a Mac for that.
You can use objective-c under Linux - gcc supports it and so does clang (though not sure what the state of Clang is for this cpu). But there aren't a lot of libraries for an objective-c programmer on Linux. Forget all the iOS an OS X stuff. There is the GNUStep stuff that is based on Next which predates OS X. It probably isn't going to be much fun beyond learning the basics of Objective-C.