By default images get put in tree of directories, two levels deep, with two very short seemingly random directory names. See this in action e.g. this image on the commons wiki (Note the /1/1c directories in the path)
Actually it's not random. It's hashed. I think if you name your file
image_filename.png then MediaWiki will expect to find this at
I say that because the md5 hash of "image_filename.png" begins with "55". You can read about how this works in the mediawiki docs about $wgHashedUploadDirectory.
So you could try FTPing them there, but this seems a bit of a messy solution.
If you set the config setting
$wgHashedUploadDirectory=false then files will have a more straightforward location
images/image_filename.png so that could be worth a try. Actually I think the hashing thing is to help wikis cope with gazzilions of images, so not really needed for most new MediaWiki deployments.
However you should also note that MediaWiki will try to generate thumbnails at various sizes. It will do this for display on your page if you specify a display width, but also for special views such as "gallery of files".
So all said and done, you might find it easier to enable file uploads, perhaps temporarily, or just for the sysop users.