Seems like it should work. Another commenter said that for their dash, they had a site that they kept open in the Kindle browser.

Although I did notice some weirdness with using the browser. I have an HTML endpoint up at https://kindle.mariannefeng.com/, and for some reason whenever I tried to go to that page using the Kindle browser, it returned a message about not being able to load the page. And I don't even think my page has javascript.

A long time ago I made a smart home automation web page for my Kindle, so that should definitely work.