I suspect that Rangel made a political calculation simply to ignore the proceedings. The Constitution does not allow the House to bar duly elected members from sitting. The Constitution, however, permits expulsion, but this requires a 2/3 vote of the entire House.
Although President Obama subtly suggested that Rangel should withdraw from the election, Rangel ignored Obama and eventually won. Now that he has won, Rangel probably believes that 2/3 of the House will not vote to expel him.
The House, however, could impose a lesser sanction (such as censure) by a simply majority vote. If Rangel's calculations are correct, only the voters in his district can control his fate. They have recently spoken on this subject by electing the 80-year-old Rangel to another term.