The short answer is possibly.
If your book is set up, and everything is perfect, and you’re using the right template, yes you can. But if there are any errors at all, that can really impede a reader’s experience. But it is, of course all down to the choices of the author.
Free conversions can happen at Smashwords (each platform only), KDP (Amazon only), though both are also OK for distributing to others, and D2D which is free of upload limitations. Do read the conversion terms though.
Of course, if you can code, Sigil lets you code content to match the site you need to load epubs to. It is epub only. Or if you are Mac, Vellum is a great option.