The Allman Brothers was a pretty iconic group, and the band should probably do a tribute to Butch Trucks, especially since he was a founding member. Ramblin' man, Whipping Post and Midnight Rider are pretty well known and Trucks had a lot to do with the sound, so he as well as others in the band deserve a tribute.
Yes, the Allman Brothers should do a tribute for their bandmate. They are an iconic band. To honor their bandmate would not only be a great moment, but it would help commemorate the memory of their legendary drummer. Many bands have said farewell to members in similar fashion. It'd be honorable.
A tribute is always great, especially for the fans. It's a great way to honor the drummer and his fellow bandmates while allowing the fans of the band to join in on the rememberance. I think every band should hold tribute shows when a member passes away, to give the fans closure.
A tribute is done by fans and other artists, not the band or the artists themselves. The band should not do a tribute. It should instead continue to play as usual, if it desires. It my find another drummer or it may continue with the members of the current group.