With Sublime SFTP, yes you do need to have files locally. Having files locally provides nice performance with all of the GoTo commands in ST2. It does also have some integration with version control systems, but if you are editing remote files, that probably isn't that important.
If you are on windows and want to edit remote files you can work with WinSCP and its synchronization feature or buy something like ExpanDrive, however I've always found editing files over ExpanDrive to be pretty laggy.
For Linux you can use the fuse sftp filesystem to mount an sftp connection as a folder and edit from that.
On OS X, As dan mentioned, Transmit can mount remote drives, and ExpandDrive can also. I think ExpanDrive on OS X tends to be a bit more performant than the Windows version.