It might kill him if he touches the radio chassis when the rectifier
fails. The stink is from the gas seleniums give off when they short.
Since the rectifier is in the power supply (across the AC line) and has
the full line voltage across it as long as the line cord is plugged in
(whether or not the radio is on), if it shorts it will likely put the
chassis at line potential (until the fuse blows). Another way the guy
could do himself in in a big hurry would be to touch the chassis of an
AC/DC radio and a grounded surface, such as a radiator, both at the
same time. Just a couple of thoughts.