It entirely depends on the specifics of the case that you are refering to. Clearly, if the legal documents draw attention to some kind of framework of law such as the UN Human Rights, then it may be that these documents can prove useful. However, it may actually be that such documents will not help the case as they are not recognised as being relevant to the US framework of law.
No way to answer your question as stated, as it is much too broad. Different situations, involving different parties, with different circumstances shaping the particular legalities being considered in the court - all these variables would impact the value or worthlessness of documents prepared outside the US, just as they impact the worth of documents prepared domestically.
I am not sure what you are referring to, but I would not say any legal document prepared abroad would give an advantage in most circumstances. US courts prefer US legal documents. Documents prepared abroad according to US standards might be cheaper, but if they are not correct than the courts will likely throw them out.
I assume you're asking about the trend towards having legal documents prepared abroad so that the clients do not have to pay American lawyers' high fees for the grunt work (so to speak) of preparing basic documents. So, this is not an issue of documents that have to be translated or that have been prepared with the needs of a different legal system in mind. It is just an issue of whether it is better to pay offshore lawyers to do a job that is currently done more often by American lawyers.
If so, the only real benefit here is financial. It is not as if the lawyers in other countries will do a better job, it is simply that they will do it for less than an American lawyer will. These documents will not be advantageous in terms of helping a side win its case. They will be advantageous, though, in financial terms. Basic documents prepared abroad will be an advantage in that they will presumably be just as good as the documents prepared in the US, but will cost less.
If the papers offered are from a sovereign nation with whom the United States has diplomatic relationships, any document properly executed and authenticated in that country will have the same legal effect as if drawn in the United States. This applies to birth certificates, divorce and adoption decrees, etc. The only possible legal hurdle would be authentication; however there are procedures in place to handle even this. Normally contact with the country's conusel or embassy can provide the necessary authentication quickly and efficiently. There is no advantage or disadvantage either way; nor is notarization and official titles an issue. If the issuing authority in that country had the authority to issue binding documents, then they are binding here as well as there. To construe documents otherwise would needlessly and hopelessly complicate the judicial system. Once the document has been properly authenticated, it is entitled to the same weight in U.S. Courts as it would be if offered in courts of the issuing country.
I think that you probably need to offer some level of specificity in this question. From an overall point of view, I don't think that American courts reject foreign documents, or documents prepared abroad. That being said, I am not entirely certain that documents prepared abroad would be an advantage in an American court. If the proceedings are in an American court, some aspect of American law is being tested. It has been my experience that American courts have a less difficult time interpreting and accepting into valid evidence papers and documents that have been prepared in America, as opposed to abroad. Documents prepared abroad need more explanation and analysis in court and must always be viewed with a sense of authenticity and originality needing to be substantiated. Documents prepared in American courts have some level of commonality in preparation, lexical familiarity, notarization, and titles of presiding officials. This is not to say that documents prepared abroad are not going to be accepted. Rather, it is to say that from the most overall point of view, I don't think that documents prepared abroad present an automatic advantage.