It is acceptable to make two versions of a web page, one for accessibility and the other for visual impact. There would be a screen reader specific link for the accessible page.
It is acceptable
"Acceptable"? In general, no. But it is legal (from a conformance perspective) to do so as a last resort, but it's generally frowned upon.
There's some good information on "Understanding Conforming Alternate Versions".
There's also a nice answer on stackoverflow. In particular, this analogy:
My own view is that going to lots of effort to provide (and maintain) alternative versions doesn't really amount to discrimination, but it doesn't aspire to inclusion either. Imagine a public library: an old building, with steps leading up to a grand front entrance. Pedestrians can stroll inside, enjoy the beautiful atrium, see posters about current events, talk to a librarian, or just go straight to the books. A wheelchair user has to go to the rear entrance, then ring a bell for a librarian to come and let them in. No fancy atrium to enjoy. The librarian has to let them out again, too. While the library is accessible for wheelchair users, the experience is a bit second-class; it's accessible by "alternative accommodations". Ideally the grand front entrance would be accessible to wheelchair users, but the architecture has a protected status. Websites are easier to improve than buildings, so it's better to avoid alternative versions.