Not any frequency, the radios have physical limitations that only allow them to transmit on a small range of frequencies. They can certainly cause interference outside of the bands they were designed to operate on, though.
Take an ILS (instrumental approach) frequency 108Mhz. Any piece of wire of around two feet (half dipole) can be a pretty effective antenna at that frequency. Say, headset cable + an output cascade of the amplifier self-excited at this frequency? Doesn't happen in real life, but still...
I am not sure how much effect this has, but it's something to keep in mind.