Hamish, it would depend on how large the new file is, compared to the overwritten one. If the 'old' file was bigger than the 'new' one, there will still be areas of the 'old' file that have not been physically compromised - just not accessible through normal means. Typically, overwriting a file with a 'blank' leaves still most of the old file's sectors untouched...

...until the newly 'freed' space gets taken up by some other file of course, or one does a 'defrag'.