Yes, they could be excluded at the Port of Entry and sent back home. But more likely than not, they will be paroled in to the U.S., their green card taken, and then scheduled to go before the immigration judge to fight the charges or apply for some waiver if one is available.
I STRONGLY suggest hiring an attorney now with both criminal law and immigration law experience. These are complicated cases and any little thing could make a difference. You can look for one at www.ailalawyer.com. Let me know if you have any follow-up questions.
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