Sure, it is possible. Already the price of each digital currency is different in each exchange. It isn't possible to have the same price in all of them, because the demand-supply determines the price and accordingly, the price is different in every exchange.
This is called ''scalping'' and is a way to make some profit. But, the prices are always variable, that's why earning is risky with scalping.
Yes it is very possible to have differences in price across exchanges because there is no central authority that sets or regulates the price, rather each exchange comes up with their rate based mostly on the demand and supply. However arbitrage is the right word and scalping is something else.