Sometimes, and the failure mode is instructive.
It works when the activity really is localised to a contiguous region that folds the same way on its own. Semax is the best case here — a genuine registered medicine came out of it.
It fails when the activity depends on the whole molecule's shape, which for proteins is more often than not. A fragment can be the right sequence and the wrong conformation, and then it binds poorly or not at all. It also usually loses whatever stability the parent had.
AOD-9604 is the honest test case: the design worked in the sense that the fragment did separate the fat activity from the glucose problems, and it did not work in the sense that the trial did not show enough effect to continue. Both halves are real.