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Unless you can show a high volume of travel (ie elite status on another airline) and are wanting to become a new loyal customer, United will likely not be amenable to waiving its rules.
Airlines like to lure customers to be faithful by offering the mileage programs, BUT they are stingy when it comes to awarding miles. Even if you have elite status, they are not quick to bend the rules when it comes to deadlines.
But as Choster mentioned, never hurts to try (a couple of times ;-)