That would be an excellent way for the cowardly senators to avoid having to go on record and still get rid of Trump. Feign a family emergency, even a positive Covid test and have to go into quarantine, etc., anything to get out of attending and having to vote.
If a significant number of GOP senators were to do that, it would probably be fairly obvious to Trump-supporting Republican voters that the senators were just manufacturing excuses not to vote for acquitting Trump and they'd hold that against those senators when they stood for re-election.
I think there's a better way for Republican senators to skip out on the vote than feigning a family emergency or similar excuse. They could speak out loudly about how disgusted they are with this second impeachment, how they think it's unconstitutional and just a political sham the Democrats are pulling -- and how they refuse to dignify such an unconstitutional sham by taking any part in it. That allows them to skip out on the trial and the vote, without having to vote either to acquit (which would tick off a large number of voters, many of whom would likely remember that vote come re-election time) or to convict (which would tick off a large number of voters, many of whom would likely remember that vote come re-election time). And it allows them to do it in a way which they can make sound like they're taking a strong and courageous stand against the outrageous partisan shenanigans the Democrats are pulling.
If 10 of them join together to boycott the impeachment trial that way, the number needed to convict drops down to 60, so Democrats would only need to convince 10 GOP senators to vote for conviction. And if 13 were to take part in such a boycott and 3 more felt they had to quarantine, the number of votes needed to convict drops to 56, so only 6 GOP votes for conviction would be needed...
Neither the constitution nor the senate rules on impeachment require all 100 senators to take part in the trial. It's possible for senate leadership to choose to insist that all senators be present, and to send the sergeant-at-arms to round up and bring in anyone who isn't present, but the senate leadership isn't required to do that. This is an instance where Mitch McConnell and Chuck Schumer might both feel it was more important to respect the choices of senators who felt compelled by their consciences to boycott the proceedings than to order them to show up or to penalize them for their absence.
Republican love to avoid having to vote on the record on controversial matters, and Mitch McConnell during his time as majority leader loved to find ways to allow GOP senators to avoid having to vote on the record. These past 2 years, for example, McConnell repeatedly refused to bring up for a vote (or even for senate consideration) numerous important pieces of legislation passed by the house (such as
the HEROES act passed by the house way back in May), sparing Republican senators the difficult choice of voting for a popular measure championed by Democrats (thus giving Democrats in congress a victory which could have earned them more votes in the 2020 elections) or voting against a popular measure championed by Democrats (thus giving Democrats a strong weapon to use against them come election time). Boycotting the impeachment on the grounds it's an unconstitutional sham would once again allow them to avoid having to vote on the record, so it's something McConnell would quite likely be happy to support and something a good number of GOP senators would quite likely be happy to take part in.
