Actually, no they are not. trump's defense is only allowed the time that the Senate is willing to give them. That was made clear to Clinton. In general, the Senate is supposed to be fair, but there is absolutely no oversight of that. The Supreme Court has no right to review the Senate's decision.
The precedent on this is Nixon v US, which oddly has nothing to do with Richard Nixon. Judge Walter Nixon was impeached without testimony being heard in front of the entire Senate, and without being given much chance of a defense. He sued and was told that the Supreme Court had no say in the case whatsoever. There were no dissenting opinions. Not one judge found that he had a right.
It is a political process, not a legal process, and certainly not a criminal legal process. Think of it like a confirmation hearing, where Republicans have been known to refuse any statement by the appointee, and to unconstitutionally refuse even a vote. The problem Democrats have is there is no one to appeal the Senates acts in confirmation hearings, and there is no one to appeal in impeachment hearings either.
If Schumer cannot get the votes to convict, he can always put off the vote for as long as it takes. That is not success, but it is not failure either.