I have never thought to try it. The wood does not have qualities I associate with good smoke wood--brittle and with a very high oil content. All parts of the trees are used medicinally in South America (and hence their name in most places where they grow here: Brazilian (or Peruvian) peppertree). Many people find the leaves, berries and wood irritating. Whether that possibility would extend to burning wood I don't know--possible, it would seem, as it is so resinous.
They are invasive here in Fla. I hate the things and have spent years ridding my property of them. I have two that just keep returning; the many others I find and rip out before they establish.