I wanted to add rich snippets for my products pages. However, the information required in the elements are not particularly compatible with my current HTML. Is it ok to make the rich snippets all hidden display, so it doesn't effect my HTML?
No. Serving up content only for the benefit of search engines is a major violation of their terms of services and will result in penalties for your site up to and including banning. You should refactor your HTML to be compatible with the rich snippets so you can take advantage of them without doing the exact opposite of what you're hoping to accomplish.