I know it can be possible. Actually, not sure if this falls into the mail order bride category but I recently read an article in the newspaper about a growing trend in Taiwan. Some successful businessmen are turning to Russia for brides. The way it worked is a bit different though - it's not your typical mail-order so to speak. They put in a deposit and then they take a 8-week trip to Russia (that includes all the countries that belong to the former Soviet Union) and go on dates with these women. If both sides genuinely like each other, then they proceed to have the wedding in Russia (signing the papers) and then after the Visa and what not are ready, the bride officially moved to Taiwan and have another wedding (the real formal one). The article included several success stories. There were definitely some difficulties at first because it was a culture shock going from Russia to Taiwan, not to mention there were cultural differences and language barriers, but most of these marriages seemed to work out because the men are quite successful, very well-educated, very open-minded and are open to the idea of different cultures. The fact that the marriage was not conducted through your traditional "mail-ordered" ways but was instead done through actual dates and interviews also helped.
Personally I wouldn't want to do it, too much money and risks involved.