Wont work first they must be capped to have a fighting chance to work secondly because they are so exactly joined at the ends they would produce a coplanar face. Wich is bad because then it gets into the precicion of things and that dont work, the solution must be apparent without precicion issues (se maya tries to find the intersection at the ends because it thinks there sould baybe be one).
I mean im totaly aware that most of youy dont get booleans to work because you asume the computer has unlimitted computationa precicion wich it does not!
So for exampe dont try to boolan boxes that share one face for example, its one of those things that might or might not work! They might never intersect only you would think they do but in reality theres a difference of 0.0000000001
This one is easy extract the ends and booean the mids than join the ends back, and merge. Works i just tested (only for some reason it wanted to use a intersection isnstead of a union oh well they sometimes get labeled the worng way...), and no the they dont need to be capped no problem theres no chance of accidental intersection here.
By the way boolean doesnet allways prduce the worlds greatest geo like in this case! You mught want to split the result if you need quads for the end output (or tris)