One of the issues (faux issues, really) raised by Republicans against the use of "hearsay" may come up in the Senate trial also. Given the strategy that the White House and the Senate leadership are planning, to minimize any evidence at trial at all, we can expect a lot of "hearsay." But should that bother us? Black argues not, and I'm inclined to agree, although to assume that members of the current Senate are more prudent and insightful about the credibility of evidence strikes me as--well--a stretch. Here's what Black says on the subject:
In an ordinary trial, for example, we exclude what we call “hearsay” evidence—testimony by one witness that another person, not a witness, told the witness that something had happened. We exclude evidence of the defendant’s character, unless he himself seeks affirmatively to establish his good character. And so on through a considerable range of technicality. Here, I think, the sensible answer comes clear. These technical rules of evidence were elaborated primarily to hold juries within narrow limits. They have no place in the impeachment process. Both the House and the Senate ought to hear and consider all evidence which seems relevant, without regard to technical rules. Senators are in any case continually exposed to “hearsay” evidence; they cannot be sequestered and kept away from newspapers, like a jury. If they cannot be trusted to weigh evidence, appropriately discounting for all the factors of unreliability that have led to our keeping some evidence away from juries, then they are not in any way up to the job, and “rules of evidence” will not help.
Black, Charles L. & Bobbitt, Philip, Impeachment: A Handbook, New Edition (p. 18). Yale University Press. Kindle Edition.