There will be republican money pouring into the districts in question. Over and over again voters will be reminded that their rep chose to run away rather than vote on (choose a topic), etc.
While the dems are away, things can be talked about, things that the dems say are important to them.
I doubt that would matter. Notice the DemocRATS only have the minmum number of holdouts to block a quorum? I think all the Senate DemocRATS supported this action. Only the senators with the safest seats participated while leaving more vulnerable DemocrAT senators in Austin so they could have political cover the next time they run for reelection.