Only if it's poorly designed (leaks local oscillator frequency back into antenna) and not shielded.
Modern receivers use quadrature sampling detectors rather than traditional superheterodyne. In that setup any leakage would be on the same frequency and harder to detect.
It is as good as impossible to run an oscillator based receiver that is also connected to an antenna that does not radiate. That's nothing to do with poor design, it's just physics. Zero coupling does not exist in practice. By design the mixer stage sits pretty close to the initial amplifier and it will result in some of the oscillator energy making it back to the antenna circuitry. FWIW I built a ton of transmitters and radio gear in my teens, it is pretty easy to take a theoretical stance here and declare that anything that leaks is not designed properly but that's about as 'true Scotsman' as you could get.
Note also with a highly directional high gain receiver that tiny bit of radiating energy is very detectable. It's just going to feed into background noise for most receivers so no one cares. But it will be detectable by a motivated hunter with the right equipment.
