Yes, but it's not quite that simple. It is easy to characterize a pure, unshielded sample of a radioactive substance -- I can tell you by the spectrum in what plant and when fissionable material was made, if a previous sample is available. Shielded material of unknown source and purity is another matter, and specific shielding can be used to mask the apparent identity of a radioactive substance. Simple screening instruments detect the presence of gamma radiation, but more sophisticated techniques and confirmation of no intervening "artful" shielding are required to positively identify the type of radioactive material present.

That being said, however, it is simple to tell if a person presenting themselves as having had a Nuclear Medicine procedure has a point source of radiation (possible smuggling), or whether they have the expected distribution and characteristic radiation of the radionuclide tracer used in their procedure.