Folders won't get erased when overwriting the files. Overwriting the existing Elgg version with a newer version will only replace the files included in Elgg core within these folders, i.e. any 3rd party plugins in mod or any additional files in _graphics or elsewhere will stay untouched. Also, the files engine/settings.php and .htaccess won't be replaced as they are not included in the Elgg zip archive. So, your site should continue to work after overwriting the files and running upgrade.php. If you want to be sure that no obsolete files/folders remain when upgrading your site you could erase the old version (only Elgg core) before copying the new version on the server. That's what I do normally: I erase all files in Elgg's root folder except .htaccess. I erase all folders except engine and mod. Then I erase everything within the engine folder exept settings.php and all bundled plugin folders in mod. Now I can copy the new version into the Elgg folder being sure that now obsolete files remain. Last thing to do is to check any possible updates necessary in settings.php (compared with settings.example.php) and .htaccess (compared with htaccess_dist), then running upgrade.php. Done! Of course, this will only work easily if you haven't made any changes in any Elgg core files you would need to re-edit into the same files in the new Elgg version.

If overwriting the files / directories fails for you, this might be caused by the tool you use for moving / copying the files. First, try to "copy" instead of "move" as it might only be a matter of file/directory access permissions. If this also fails to work you might need to use another tool for copying the files.