Alibaba has to remove counterfeit goods to go public, or it will be a failure. If the company does its proper diligence, this should not be a problem.
There is precedent in companies that weren't legally strict becoming more strict when moving forward. Crunchyroll is an Asian media site that used to take user submissions and had a lot of bootleg Japanese anime and drama content. Once it formed partnerships with production companies, all that material was removed, and it has been legitimate ever since. Alibaba can do the same thing in the physical product realm.
They should be able to remove the counterfeit goods from its site before it goes public. Removing them is going to help them get more business due to word of mouth and trust in the company. With all the press they are getting about going public, selling counterfeit goods is only going to hurt the company down the road.
No, Alibaba will not be able to remove counterfeit goods from its site before the company goes public, because Alibaba does not care about the counterfeit goods that are sold on its website. People's attitudes towards counterfeits are different in China than they are in the United States. They do not have a problem with copyright violations that we do. The system in the US is better.
Will Alibaba be able to remove counterfeit goods from its site before the company goes public? I do not think so, the problem is there and it's already known. Today and in today's world the media is quick and fierce. They will jump on you before you realize you have a problem.