I haven't been able to find much in the way of alternate primary sources for a Dyson–Harrop satellite. The NewScientist article, which is the proximate source for e.g. Wikipedia, references this paper in
the International Journal of Astrobiology. I don't have access to this journal, but more-technical commentary on it is available here.
The wording of the analysis as well as common sense tell me that the satellite is moving slower than orbital velocity, possibly not at all, and is buoyed up by reaction from decelerating the solar wind. Indeed, this is unavoidable. So, the first problem, I should think, is that your spaceship will have an additional radial thrust vector (though depending on the transfer orbit, this may not be undesirable).
The second problem is whether the scheme actually works. I'm skeptical that the system provides enough power to maintain its own magnetic field, but I don't know enough to reason about that scientifically. From an energy-balance perspective, it checks out okay though (energy is captured from solar wind, and in-principle there's nothing wrong with expending some energy to do this). Addionally, I'm skeptical the amount of energy to be gained is in the megawatt or even kilowatt range. Perhaps this is discussed in the journal article in more detail.
It's worth noting that mass is reasonable. The copper wire is ~200 kg, which is about 1/5 the weight of the Dawn ion spacecraft. I'd bet this is comparable to the mass of Dawn's solar panels, which produce 10kW (or ~1/100 the power of this scheme, if it worked).
As far as I've analyzed, nothing here is a definite deal-killer. I'd say it's plausible. In-particular, if you believe the claims for a satellite, there's nothing preventing you from using it to power a spaceship (which is after all merely a satellite designed for SOI changes).
(N.B. I'll agree in-principle that physics.stackexchange is a better fit for this question, but in-practice the only nontrivial questions they seem to favorably receive are related to GR/SR and, in-particular, any speculative applications of Physics are right out.)