“If they hear it, it’s likely they will reflexively reply the Constitution permits the Senate to make its own rules.”
That is what the Constitution says, whether we like it or not.
But they cannot completely negate the Constitutional right of the house to impeach and have a trial. While it is held “in” the Senate, it is not the Senate who holds the trial. They are only a second party to vote a verdict to give fairness to the accused. And vote to remove or not.
The trial 100% belongs to the house as part of their right of impeachment and a third party, the chief justice of SCOTUS oversees the trial. Constitutionally the Senate is absolutely Constitutionally obligated to allow this trial on their floor.
They can however vote him innocent if they like AFTER the trial.That right is indeed theirs and theirs alone. That is the only time Senate powers come into play at all with this impeachment process.
If SCOTUS rules this way, it is an unconstitutional ruling. The Senate CANNOT set rules for the house in how it holds an impeachment proceeding or deny the house’s right to hold an impeachment trial.