The simple answer is NO, an SEO company cannot run your business, nor they have the knowledge or domain expertise in running operations of a company, else they would be running a similar one like yours.
Good SEO Agencies are experts in knowing how to out-rank your competitors and rank for relevant keywords, web users search for in search engines like Google, for example, a web user searches for a keyword “cheap holiday deals” in Google.co.uk and your website is ranking on page 1.
Approximately 17,000 people search this keyword in a month in UK and the chances of some clicking a website from page 1 is around 70% (12,000) have a chance of visiting your website, a 1st rank position is worth 30% of the clicks --- 5000 visits.
With 5000 people visiting your website how many will buy products or services on the website????
That depends on many factors like kind of product/service, price, quality, trust, brand and reviews etc… which a SEO company cannot control, but one can generally predict more visits would bring more sales.