Not necessarily. A small envelope stained with a drop or so of a solution containg radioisotopic iodine, chromium, cesium, etc., etc. could wreak havoc whether or not significant levels of radiation were involved......
Not with anyone who knows diddly about radiation dosage, radiation effects, and health physics. Do you suppose that the conveyor lines in post office sorting areas aren't already equipped with radiation detectors. AT MOST, an envelope with your "drop of radioactive solution" MIGHT give some dose to the guy who picks it up out of the mailbox and carries it back to the post office, but I would suspect that any such exposure would not exceed current limits for "allowed occupational exposure".