I was curious if using classes in h1 tags affects a sites SEO ranking?
I wouldn't think giving an h1 tag a class would make much difference. Classes are used to style specific pieces of html. Google doesn't really care how its styled, but an h1 by nature has more weight in search engines than other tags.
I think it doesn't make different if you use style in H1 tag, because Google only require the presence of H1 tag in your website. But not only the presence it should be there surely if you want good ranking result of your website.