Still, if America fell right now, would our culture and ideologies influence the world as we know it for millennia like Rome? Likely not.
Granted you are correct about our global economy, however the influence is mainly our products and alliances, which is completely unlike the Roman Republic, Monarchy or Empire.
The English language is growing to be a more common language around the world, although for both some influence and the fact that, along with Mandarin Chinese, it is slowly becoming the economic and business language.