If you are happy with continuing to use the external links the answer is yes, because html can use external links, most likely without change.
To embed the external images into the static file you will possibly need to retrieve them first into your wiki, or a utility one set up to do this. Then make sure the save static html file includes them (I think it does).
The thing about exporting as static html is there are a set of templates defined in tiddlywiki to do this. If they do not do what you wish, you can clone and save/export with a custom template with any desired changes.
Although as all images are already external in your case just test by transuding some images in one tiddler and export it.