Google does index PDF files. So if you have a script setup that converts your pages into PDF format and the design looks very sloppy, Google might notice this. I could potentially foresee an issue arising in which Googlebot begins to crawl many of these PDF renderings and reduces a site's design because of it.
Let's say that your website has a design score of 10/10, and your PDF renderings have a design score of 0/10. If Google crawls the same number of PDF renders as it does webpages, the average score of your domain might then be 5/10.
The Googlebot algorithm does factor in website design, UX and mobile friendliness into its scoring system. And so if it attaches the design of your PDFs into that score, it could diminish your site.
Google does seem to like PDF files, and so rendering PDFs could potentially give you a ranking boost as you're giving Googlebot extra content to digest. But it's possible that poor PDFs could hit you as well.
Also, anything on your site that reduces a user's experience could negatively impact your SEO. Let's say that your pages have a large print button on them which causes a high click through percentage. And your print PDFs are a bad format. This means that a high percentage of users are going to have a bad experience because of the bad formatting. On the other hand, if the print button is obscure and small, less people will have a bad experience. Since user experience is a ranking factor, how this is implemented can effect you.
I haven't seen any studies on PDF design affecting SEO, but there is a good chance it is correlated to the same principles of overall design and UX since it does affect the user experience.