If the software attempts to find multiple features and time each of them, then it is less likely to plot only a single transmitter, but rather might indeed plot combinations of both transmitters, resulting in junk.
In fact, I was wondering about exactly this so I attempted to "find" WWV on 5 MHz, 10 MHz and 15 MHz with receivers on the west coast of North America in the presence of WWVH (and passband narrowed to ~100-200 Hz so that differences in the male voice on WWV and the female voice on WWVH were reduced and the focus was on the carriers only). I don't have the results available right now but let's just say that things became "confused". It seems to me that as a general principle with TDoA, anytime there is a significant amount of skywave propagation present, the derived result varies quite a bit over time (see more on this at the bottom of this post). In this case, this was worse than I expected. I suspect (but was not able to prove beyond a doubt) that the presence of WWVH confused the algorithm.
Could it be used to find the ham jammers? Maybe, but remember what I said about the 30 second samples. Transmissions from multiple stations, even if one at a time, that have handoff times inside that 30 second window will likely mess with the system. So if the jammer does not stay on the air for the entire sample time that will probably result in errors, jumbled combinations of the data for the jammer and jammed stations.
There has been some discussion about allowing for sampling intervals shorter than 30 seconds for reasons like this.
Getting back to what I mentioned before, skywave propagation is a big confounder here - it will cause a fair amount of variation from location attempt to location attempt. (This makes sense to me as the ionosphere will produce significant variable amplitude and phase shifts when the signal returns to earth.) Also, weak signals are more difficult to get a clean result on. Contrast this with strong, groundwave signals, which are relatively easy to locate. I was able to locate BBC - Droitwich (198 KHz) and RTL (234 KHz) to within ~10 km using only 3 receivers and I was able to repeat both using a second completely different group of receivers as a check. I did the same with WWV on 2500 KHz (only one set of three receivers though). However, 5, 10 and 15 MHz are not trivial and derived location was highly variable. I assume that this is due to the significant skywave propagation there.
All this means that HF pirates probably have little to worry about by the Kiwi TDoA network. You are quite unlikely to be successfully located down to your house. (I can't comment on what the authorities might be able to do though, so beware.) A MW or LW pirate might want to pay attention though.