That depends on how heavily shielded they are. Since plasma based weapons (blob turrets) were the staple of FS ships for quite a while this should be taken into account.
Blobs are self-contained plasma weapons, which
may actually be possible, but projecting an incredibly long magnetic field out into space to contain a thin stream of high-energy plasma would have effects regardless of how heavily shielded your electronics are. For starters the shielding necessary to protect your electronics wouldn't be all that much less than that to protect you from the plasma. Then you get induction in any metallic object the field comes in contact with as it extends, and rather impressively at these power levels.
As an addendum, notes from FS1 and FS2 about effective anti-shield weapons suggest that kind of focused magnetics would be absolutely devastating to shields. Yes, beams pass through, and that might happen, but there should also probably be some serious loss of power.