Invoke Adobe SVG Viewer find function

Is there a way to achieve this with an onclick event from an html page with an svg image embedded so that the user can search text in the image?

No, not exactly like you may be thinking. But you can use Javascript or you can use XSLT to search the text in the SVG document.

XSLT example, check this out:
http://www.w3.org/2002/05/svg2stuff.html

If you want a specific Javascript example just ask.

Learn SVG - http://learnsvg.com