Your assumption is not too unlikely, but with bitcoin we have no option for high speed trades between exchanges, except if they were conducted over an interchanging platform off-blockchain.
Bitcoin arbitrage is meh, the transaction time is slightly too slow to allow consistently efficient arbitrage.
One does not need to move funds in real time between exchanges to do arbitrage. Or maybe not at all.
An arbitrage opportunity occurs whenever someone posts a bid at one exchange A that is higher than the lowest sell at the other exhange B (or someone posts a sell at B lower than a bid at A). At that moment, an arbitrager at A, if he became aware of that situation before other clients, can sell into that bid, while his collaborator at B (need not be the same person) buys into that ask. Both traders will then profit, relative to the mean bid-ask price that will result from their actions. These trades are internal to the exchange, and therefore instantaneous - they do not appear in the blockchain at all.
In fact, one could view arbitrage as two people trading, each within one exchange, with the usual "buy low, sell high" rule. The difference is that, by knowing the other exchange's order book before other clients, each trader can, in a sense, peek into the immediate the future - he gets a hint as to whether the price at his exchange is currently "low" or "high", relative to the mean price that the arbitragers themselves are about to fix.
With those hints, both traders can consistently "buy low, sell high" and keep increasing the total vaue of their accounts. It does not matter whether price is in an increasing or decreasing trend, or varying randomly within a band; as long as the bids and asks get posted independently at each exchange, these occasions are likely to happen.