There is conflicting information on the web regarding the edibility of this plant (for humans), and most of it doesn't seem to be from any major reputable scientific source. It is not listed in any of the Herbal Dictionaries I've checked, including Wiki's list.
Either way, from what information is available, Tradescantia zebrina is not considered one of the culinary herbs, and its use has generally been restricted to medicinal purposes, in the same way as, say, St. John's Wort or Valerian. Considered to 'strengthen the blood' (the jury's out on what that actually means, I've no idea, sounds like nonsense to me), and has been used as a treatment for colds, tuberculosis, high blood pressure and 'problems of the uterus' (again, ?). Some people may have a strong reaction to this plant, either by contact or ingestion, depending on their individual sensitivities. It is, though, perfectly safe for reptiles to consume, though likely only in small amounts:-
As for the taste of any tisane or tea made from its leaves, I'd imagine most of the pleasure in taste will come from the high amount of sugar and citrus juice rather than the Tradescantia leaves themselves, judging by the recipe given in another answer (reminds me of the recipe for 'nail soup', an old Serbian joke...) So, ultimately, no, I don't think you could consider Tradescantia zebrina a 'crop' plant.