No, HD has NEVER scanned your system to determine the "correct" directory for HDE files. There is no "correct" directory - it's wherever you decide to save them.
The first time HD runs, it has no idea where your files are -- it defaults to the directory that it's running from. You point it to the directory that you saved your export formats to (when you downloaded them from this site, or wherever else you got them) and it will remember that directory going forward. If you download other HDE files to a different directory, you'll need to point HD to them if you want to see/use them.
This is no different from any other program you have on your system.
And no, "installing" or "uninstalling" HD will have no impact on this. The only thing that will change the above process is if you delete the directory that HD is saved to/run from as doing so will delete your appPrefs.xml file, which is where HD stores information like the last directory used for HDE files.