While you can be successful doing business online without SEO--or even a website for that matter--there will always be limits to what you can achieve. SEO is nothing more than the act of marketing your website so searchers can find you. Today's SEO encompass many other aspects of digital marketing. How you go about online marketing depends on your budget and what areas you specifically want to focus on.
Holistic digital marketing can be quite expensive, but there are a lot of things you can do to start pushing yourself forward without a huge budget.