Do you plan to run something more serious than github, basecamp or shopify? Usually it is not rails, which is the bottleneck, but the architecture of your application.
As a matter of fact, yes. Not as big as GitHub, but bigger than Shopify. So the choice of application server matters, as well as how easy it is to scale and provision that server.
Shopify has 800,000 customers, 4,000+ employees, and handles over $40,000,000,000 per year. And you're building something from scratch, starting today, that is going to be bigger than Shopify in a fast enough timeframe that your Rails server today is the biggest concern?
Something doesn’t add up: You have have a high profile project that is bigger than Shopify (!) but you ask a question that seems like the first question you should type into google to research this if you were interested.