Neutron stars are sometimes detected by their extended magnetic fields, or by radiation from particles interacting with the fields.
This question is about the possibility of neutron stars in small orbits about each other forming a closed magnetic flux that is not extended far enough in space to be detected by the usual methods.
Difficulties occur when the magnetic poles are not aligned with the rotation axis.
Will Close Binary Neutron Stars Become Magnetically Aligned?
I think it unlikely, any effect of one star on the other will cause the spin to precess but the angle between the spin and magnetic axes is likely to remain fairly constant. By the time they get close enough to have a strong interaction, gravitational tidal effects will be disrupting both bodies and gravitational radiation means the time spent in that regime is short.
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