This credible sounding newsgroup post, as well as Tony Lee's answer indicate that for most applications a "save as" ovewrite is the same as a delete, followed by a create-new as far as the file system is concerned. I can second that generalization because as as a programmer, it makes sense. If I were implementing "Save as" feature there is no reason to use a file-open for re-write API call, as this is code path would only be used in the rare case of an overwrite. A programmer is much more likely to use the create-new file call with a quick fileDelete call in the rare case it is necessary.
That said, there is no sure way to know how the progammer of the overwriting app chose to deal with the existing file, unless you can ask them, or trace the app's file system behavior with a tool like FileMon or Process Monitor.
On average, I'd guess that you are only slightly less likely to to recover a file that was "overwriten" by an application compared to any other file that was deleted followed by writes to the disk.
Needless to say NTFS undeletes are not a very reliable recovery strategy. If this is likely to happen again, Look into some sort of version control system to supplement your daily back-up strategy. Unfortunately automatic file versioning that used to be a standard feature in some Operating Systems like VMS and Netware is no longer a common feature in the mainstream market.