Whether you’re working on a General Society of Mayflower Descendants application or a Society of Cincinnati application, it’s very possible that you’ll run into records that aren’t in English. Most lineage societies are based in the United States. Do you need to have the records translated?
Not necessarily, but it’s a good idea. While many of the larger genealogy departments have staff members that read multiple languages, there’s no guarantee that they’ll read the language your ancestor’s records are in. The smaller societies may only have one person on staff, who may or may not be able to read that language. You can definitely ask, though.
If they say no, you’ll need to plan to have the record translated. A larger organization may be able to find a volunteer who reads the language and can assist. If you need to hire help, a genealogical translator (a translator who specializes in working with genealogy related documents) will be your best option. You can find translators through the American Translators Association or through the Association of Professional Genealogists.
Be aware that genealogical translating is a “buyer beware” market right now. Many genealogists who advertise language skills only have “high school level” training in that language, while many translators who advertise that they work with genealogists may not have the training in history needed to fully work with your documents. Ask questions.