No, even if a microphone had response that extended to that frequncy range (very doubtful in a mic intended for voice surveillance), it will respond to all frequencies and a simple filter would remove your jamming signal leaving the voice intact. But no one interested in surveillance would consider using a mic with response higher than the voice range so it’s a moot point. In any case, it wouldn’t work.
As to your comment regarding frequency range, most MEMs microphones have a response past 20KHz, and some even have a convenient resonant peak above 20KHz. Driving them with a very high SPL at that frequency causes them to clip sufficiently to prevent them from responding to audio inputs.
If you want to watch this kind of interference get a piezo driver and generate a high SPL field -- dangerously high, like 140 dbM, and see what the output of your mic looks like. Unless you have a very slow response dynamic mic, you are likely to see hard clipping of the mic output. And actually the only thing that saves the dynamic mic is its poor high frequency response.