Marriage to a foreigner is not forbidden, but it is not encouraged, and it also has a number of its own specific requirements.
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Marriage. A foreign woman married to an Emirati national may acquire citizenship provided that the marriage lasts for at least seven years with the condition of having at least one child, or ten years in the absence of children. The wife of a naturalized male citizen may also acquire Emirati citizenship.
There is nothing in the regulations that say individuals who are in the US as visitors cannot get married. In fact, you are even allowed to come to the US as a visitor with the sole intention of getting married.