Can I rank well without doing any SEO?

The short answer to this is yes; the detailed answer is not really. Although it is possible to rank without any SEO strategy, it will be very difficult. Your target keyword will have to be very strong and relevant to your site and have minimal competition. All of your exposure will need to be through intense marketing and word of mouth. All the factors that make a website rank well are part of an SEO strategy anyway – factors like quality content, mobile friendliness, social media sharing, etc.