I doubt this is achievable, certainly not within the Rh interface. You could link the image to a popup but it would have the content of another topic set up for the purpose. As such it would not be included when you print the topic with the image.
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I had a feeling this was the case and this is how I set it up (separate topics for each image map hyperlink...these will not be included in the print output or in the TOC). I did leave the original text in the main topic with the image, though, and used a conditional tag to exclude it from online view but include it if the user wants to print the image with the text.
Now, the only issue I am having is: When I click on the image map, I cannot get the topic to popup; it opens in a new window (even though I have auto-sizing popup selected in the hyperlink properties). Maybe this has something to do with the image map itself?
Can we break this down a bit?
You said you have an image and on that image you have an image map. This means you want clickable areas on each part of the image that do something.
Where it gets confusing (at least to me) is when you say you have text on the same topic that you wish to pop up from the image map but not be seen when the topic is viewed. Only when the image map is clicked. More info is needed on that.