I'd caution you against thinking that having to press a button on a dongle means that there's a required intermediary step.
I can imagine a design where the RF signal is being generated on a very low voltage/low power device that's always/permanently on, and pressing the button enables an integrated antenna that suddenly boosts the signal to a usable signal strength.
In that case, the attacker just has to simulate a increase in signal strength if they are already tapping your signal.
Electronic design doesn't follow the same rules as physical device designs - for example, that power button on your PC, it doesn't really close any circuit! It just tells the motherboard that it's ok to let voltage through a certain electrical pathway, the computer is already permanently on and is trickling power from AC / Mains.
You can use software to tell the motherboard to activate the same way that "pressing the button" does - ie remote server control over pxe, etc.
Most cars are always on trickling power from their battery waiting to hear that signal, I wouldn't be surprised if dongle design follow the same principle.