Shouldn't be too hard, I spent half my life in Saudi Arabia, the other half in India. I work as a CSR/TSR and 95% of the time people can't tell I'm a foreigner. I'm not sure if it sounds 'American' or 'neutral' (is there such a thing?).
Ed: Kate Winslet is pretty good at doing an American accent too. Compare her accent IRL to Eternal Sunshine of the Spotless Mind. Hard to tell she's a Brit.