It is complete nonsense.
If anything, constantly tensing your abdominals will decrease metabolism, because it makes more difficult for food to pass the gut. Chronic tension in the abdominals can result in constipation.
You will not see much fitness benefits either. The abdominal muscles are no different from any other muscle. It is not possible to get much stronger and healthier by voluntarily contracting the biceps the whole day against no resistance, so why would it be any different for the abs?
The effective way to increase metabolism through exercise is to work as many muscles as possible. The biggest muscles in the body are the quads, glutes, and back muscles. So get some serious exercise and stop focusing only on abs.