Yes. These versions all use the same file system. No conversion is necessary.
If you want to open a file in FD4, Final Draft 5 and 6 allow you to downsave a script in the FD4 file format. You would go to File > Save As and select Final Draft 4 for the save type. Make sure to change the file name to create a separate FD4 file. Final Draft 7 doesn't have this function.
NOTE: All support for Final Draft 7 and older has been discontinued.