To elaborate briefly on GTO's post, the technical answer is yes, the local oscillator(s) in a superheterodyne receiver radiate enough signal to be detected by highly sensitive receivers. A good example of this is how in the UK the Ofcom "snoop vans" detect unlicensed TV sets.
On the practical side again it's Ofcom, out of 24 vans in greater London only 2 are so equipped and at any given time one is in the shop for service. The rest are dummies intended to scare the public making the whole thing a joke. Weighing all things considered in the balance the answer to the question becomes a resounding no when the weight of "I really don't care" on the part of authority is overwhelming.
Then there have always been passive receivers but that's the subject of another discussion altogether.
"If you're within a couple of metres of the person transmitting then often they will get an echo on their radio, like when you hold two walkie talkies near each other."
While completely off topic an interesting point none the less. "Often" happens when the unit is transmitting through a repeater and the digital delay in the controller audio processing chain spits out what was said usually a quarter second behind real time.
"It's happened to me once when trying to get a security frequency using Close Call in a shopping centre and the guard enters the bathroom, transmits, gets a strange echo and he walked off."
In a case like that your Close Call falsed on you with an on site repeater when it should have locked on the unit transmitting and you would have heard the squeal of ordinary feedback.
Bathroom echo? Sounds familiar, RCA Victor did it the cheap and dirty way by placing a monitor speaker and microphone in the bathroom during the recording of Heartbreak Hotel by Elvis Presley. Betcha didn't know that now didja? (;->)
YouTube - Elvis - Heartbreak Hotel