Typically Thread2 will not cache the writes locally and the two threads are independent. So generally, yes you will see performance benefits from accessing both files simultaneously.
You will also usually see performance benefits from accessing two local files that are on different disks - even if they are on the same controller.
You can often see performance benefits even if the files are on the same disk because this allows you to keep the disk busy - but to avoid thrashing the head around you need to do IO in large blocks. If the local drive is flash then there is no seek time, so having multiple threads reading/writing to it doesn't reduce performance like it can on a hard drive.
A couple of things that can affect this: 1: Windows supports "offline files" where the client is allowed to cache files of a remote file system, both read and write on a local drive. It used to be that when the client would only use the local cache when offline. I don't know if Win8 changes this.
2: "\ServerY" might actually refer to the local machine.