No, carob does not contain significant amounts of caffeine or theobromine. (Theobromine is a chemical, similar in composition to caffeine, which also is a stimulant.)
I’ve found many sources that claim carob contains no caffeine or theobromine, however a study on Caffeine and Theobromine Levels in Cocoa and Carob Products published in the Journal of Food Science found that “theobromine and caffeine levels in carob products ranged from 0–0.504 mg/g and 0–0.067 mg/g, respectively.”
In addition to tea, coffee, and chocolate, caffeine is found naturally in yerba mate, guarana berries, and the Yaupon Holly.