Answers
Does fancy text affect SEO?
Yes, and not in your favour.
Short answer
Yes, negatively. Search engines index the characters you actually used, so a styled heading does not match searches for the plain word. Titles, headings and body copy should stay in ordinary text.
The short answer
Search engines index the characters you actually used. A heading written in styled characters does not match searches for the plain word, so the keyword value is lost. Titles, headings and body copy should stay in ordinary text.
Why this comes up
It usually surfaces after a page stops performing. Someone restyles a heading for visual impact, rankings drift, and the two events look unrelated because the page still reads correctly to a human. The characters changed; the visible words did not.
What to check on your own pages
Look at the title tag, the H1 and any headings, and confirm they are ordinary characters. A quick test: copy the heading and paste it into a plain search box. If searching for the phrase does not match your own text, no search engine can match it either. Body copy matters too, but headings carry more weight and are the more common place people apply styling.