Not exactly. When it comes to the columi drops a given flashpoint will always
drop an item of a particular slot. For example, False Emperor Hard Mode always drops a columi chest piece after the final boss while the Battle of Ilum always drops the offhand. That way, if you want a full columi set, you have to run all the FPs, and not just do the same one over and over again.
The class for which the item is designated, however, is random as Abokado said. You should definitely not be Needing on items that are not for your class - that's a good way to get yourself on a lot of people's ignore lists. Greeding on it is ok, though, and you might get items for your companions or to sell if nobody else in the group needs on it.