The most important thing was not necessairly winning official diplomatic recognition for the Confederacy. The most important thing was getting the financial houses of Europe to believe that the Confederacy was credit-worthy. In other words, the great banking houses of Europe (Rothschilds, Barings, ect.) had to be convinced that if they made loans to the Confederacy, they had a reasonably good chance of getting paid back at interest. If this had happened, the Confederacy would have been able to float loans backed by cotton, and been put in a much better position to win the war.
IOTL, the New York representative of the Rothschilds (I forget his name) was generally pro-Confederate and a staunch opponent of Lincoln. But, facts being facts, he did not believe that the Confederacy was credit-worthy, and said so in a long and detailed letter to the Rothschild Bank in London. Had their reprensentative had a slightly different point of view, he might have recommended that the Rothschild Banks provide loans to the Confederacy. This would have been important in and of itself, but it also would have given the Confederates enough credibility to obtain loans from other European banking houses, thus solidifying their financial base.