I don’t believe there’s any build-in method that reports if $Text contains images. so for now you’ll need to tag that yourself, if needed.. I’m forgetful. See $ImageCount (thanks to @eastgate for correcting my error)
HTML Export does export images, but currently (I just re-tested with v7.3.1) text export does not. See more.
Attribute Browser won’t help as there are no images-related attributes of use for which to browse.
If you select multiple notes (containing images) the composite text view in the text pane will show the images. I copied that text and was able to paste it to a TextEdit new document (though text/image sizes varied a it).
I sense you might have a feature request, so it’s worth emailing in a request and your use case if you need more control over image export.