I have not tested it myself, but according to the Amazon Kindle Publishing Guidelines 2019.2, Section 13 (Creating Fixed-Layout Books Without Pop-Ups), it is supposed to be supported for fixed layout books without panels or popups.
Quote:
13.2 Text Guidelines
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Live HTML Text
In this method, the background image is stripped of text and the majority of text in the book is rendered as live HTML text. The text can be repositioned as needed for a good eBook experience. This method also allows search and dictionary functionality.
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Invisible Text Overlay
For text that is part of an image, or is irregularly sized, angled, or curved, you can capture that text as part of the background and use invisible overlay text (using the opacity:0 property in the CSS file) to enable selection, dictionary lookup, and search.
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I will add that creating fixed layout based on PDF instead of HTML would be less prone to problems.