Early Alameda strategy was BTC arbitrage in Asian markets (which is very above-board). They were definitely successful. Once that well dried up (arbitrage is usually an "early bird gets the worm" game), they started gambling on shitcoins, which is where the troubles began.
The BTC arbitrage in Asian markets was absolutely NOT very above board. He lied to get Japanese bank accounts opened and to keep them open. Transferring the BTC into Korea was against the law there. He just figured out how to do it for quite a while without getting caught.
Yes, it made money. Yes, he claimed it was legit, but it wasn't--it was money laundering illegal gains. It just sounds so much better when you call it "arbitrage".
They were definitely not successful. Anyone looking at BTC prices between NA and Korea saw the arbitrage opportunity. The fact that it sat there so obviously for so long was a testament to how impossible it was to profit from it. In fact, the whole reason for the pivot to an exchange from a pure arbitrage play was due to their lack of success.