I don't think there is anything to compel the Senate to hold a hearing if articles are passed by the House. They could simply ignore it and refuse to conduct a trial.
The founding fathers acknowledged that impeachment was a political tool that would reflect the status/strength of the parties, not necessarily the guilt or innocence of the President.
Hamilton:
"Their prosecution will seldom fail to agitate the passions of the whole community, and to divide it into parties more or less friendly or inimical to the accused. In many cases it will connect itself with the pre-existing factions, and will enlist all their animosities, partialities, influence and interest on one side or on the other; and in such cases there will always be the greatest danger that the decision will be regulated more by the comparative strength of parties, than by the real demonstrations of innocence or guilt.”
