False.
They can decline to hear the bill at all.
Sorry, I didn't consider that. Yes, the Senate can refuse to hold a trial. However, whether they would get away with it politically is another matter. What would happen is Trump would be tried in the media.
Here's the thing, the Stalinists in the house trying to pursue this coup are engaged in a severely unpopular act. They still are attempting to undo the 2016 election because they simply refuse to accept the results.
If Pelosi and her Bolsheviks were to impeach in January, the Senate would GAIN stature by refusing to entertain the farce.
This coup the Stalinists are attempting is playing to the most radical left fringes. It is a huge gamble making an assumption that the nation as a whole wants to go full Venezuela.
You are neglecting the possibility that there might well be damn good cause for impeachment. Obstruction of Justice, Election Law Violations, and accepting any type of campaign contribution from a foreign national is a violation of the law. These are not as Trump said, peanuts. They are serious crimes and are often associated with even more serious crimes. The president's primary legal responsibility is to uphold and execute the law.
Trump seems to believe as do many of his followers that the end justifies the means. Break a law here, violate the constitution there, lie, cheat, and mislead the public. It's ok, as long as you accomplish your goal. There is no excuse for this, not what previous presidents have done, what congress has done, nor how important the goal may be.