I am not a teacher.
No. "Marriage" gets special treatment, it seems. We enter into it. We do the same with contracts and the like.
Your sentence is slightly unidiomatic even with "into" (He succeeded in persuading the young lady into marriage with him.). The words are in the right order, but my American ear wants the infinitive with "persuade", and "marriage with him" sounds old fashioned: "He succeeded in persuading the young lady to marry him."