Actually, lets be fair to the Anime. Most of the characters, main/secondary anyway, were portrayed as White in the T.V. show/its sequel movie. Even to a large extent, in first two movies. Only Saito and Pazu, were obviously Asian. The Anime, in all of its incarnations, is obviously designed to be more interesting to a Western and largely White audience. So really, an Asian actress would not have been accurate. If anyone disagrees, I encourage you to go back through and watch it again. I have seen each season of the TV series 4+ times. I didn't like the first two movies, but Batou and Togusa changed little in the transition to the series. Not sure about the others. Motoko aside, as she did change a decent amount.
Oh, and since the TV series is the most popular and well known incarnation of Ghost in the Shell, its assuredly what the movie is adapting from. All of the other incarnations are so similar, it really becomes semantics.
Batuo is obviously white and has blonde hair, Asian's do not - unless bleached.
Togusa is obviously White and has brown hair, Asian's do not - unless dyed.
Motoko is full Cyborg, so one could argue anything concerning how she looked before becoming a cyborg. But, its important to note she looks white. A body/image, she chose for herself.
Borma, Ishikawa are also obviously white. In fact, Ishikawa looks more like an American Red Neck then anything else with that hair and beard of his. Trust me, I live near a large population of Red Necks. He'd fit right in.
Aramaki, is debatable. He could be Asian, but he also looks White.
Saito and Pazu are the only Asian team members and they get very little airtime, especially Pazu.
So, no. Asian's would not fit the series at all. Despite it being a Japanese anime, its so obviously aimed at Western/particularly American society, that casting the cast as Asian would alienate the fan base - aside from any truly hardcore Anime people.