I wonder if we can mess with it like we did the woodpecker?
https://www.qsl.net/n1irz/woodpeck.html
The quick answer is that you are unlikely, at best, to have any impact on the radars performance. And no impact, no response.
FMCW, or FMOP, waveforms are widely preferred for HF radar today, and FMCW is what Nostradamus uses. This preference comes from multiple advantages over simple pulsed or coded rectangular pulse (as the Woodpecker was) radar waveforms.
Below will contain some generalizations, and so errors of incompleteness or omission. Just trying to get across the general idea here, not start a math war.
FMCW occupies less bandwidth than a pulsed radar of similar performance. Yes, I know, we see these things (modern HF OTHRs) as hammering wide chunks of spectrum, but in reality they disrupt less than something like the Woodpecker did. Some people think the Woodpecker was so wide because of power levels, and while that was part of the reason, no doubt, another reason was the BPSK coding and a roughly rectangular pulse. The most common pulse width of the Woodpecker was 3.1 msec. If they used a rectangular pulse with good rise and fall times this would have had a 3dB bandwidth of well under 500 Hz, but widths at the 10 and 20 dB points would have been wider, depending on pulse shape maybe 1 or 2 kHz wide, and 40 dB points may have been over 200 kHz wide. Now add the LRS BPSK coding they used, and you spread the spectrum out even more, with the 20 dB points potentially being over 50 kHz wide and significant energy spreading out beyond that. And the 20 or 40 dB points, backed by that much power, occupied / disrupted a lot of traffic either side of center freq.
So the Woodpecker had a very wide spectrum, but the most important part was the center frequency inside the 3 dB points. If you put some energy right there in the relatively narrow 3 dB bandwidth around the center freq you could impact the ability of the radar significantly. And that is what "Woodpecker hunters" did, find the c/f and send back synchronized pulses (lean on the paddle and set the speed right on a keyer) occupying a significant portion of the 3 dB bandwidth of the pulse. Easy enough to do when the 3 dB points are a few hundred Hz wide.
But with FMCW the energy is spread out very evenly and more efficiently. This means the 3 dB point can be very wide, in the case of the Nostradamus mode being discussed in this thread, slightly over 30 kHz. But the 10 or 20 dB points don't extend much beyond that, so the total disrupted bandwidth is relatively narrow. The total disrupted bandwidth at the 40 dB points is maybe a bit under 35'ish kHz. Of course your receiver bandpass may extend it out a bit more than that.
So, FMCW or FMOP disrupts less spectrum than pulsed radar.
But, it is more immune to narrow frequency noise sources. If you key your transmitter in the middle of an FMCW chirp you will disrupt a few percent, at best, of the total swept frequency range. And the receiver processor will probably ignore or notch out that portion of the chirp, at least until the width disrupted exceeds some threshold.
Of course, you could run techniques that would impact such radars, but it is not going to be a simple OOK type of thing. You are not just going to tap a Morse key in sync with the sweeps (as some of the Woodpecker hunters did) and get much in the way of results.
T!