I'm assuming a hypothetical setup as follows: Two labs (Alice and Bob) exist. Each has one electron of an entangled pair. At Alice, the electron travels through free space towards a magnetic field of fixed orientation. When it is sufficiently close to the field, it's dipole moment will align itself to match the magnetic filed, thus being measured. This will cause the electron at Bob to anticorrelate and assume the orthogonal dipole moment. If the electron at Bob was traveling through space sandwiched between two conductors of no net charge, will the electron induce a current (even a very tiny one) in the conductor(s) as it realizes its new spin? Please correct me as to any false assumptions in the setup I have described. Thanks
No; good question though.
One way to make analysis of such problems easier is to think of quantum wave functions as envelopes of uncertainty. Classical physics in contrast beats these envelopes down into near-submission by forcing them to cough up information, so that you can say specific things about where and when something happened. Once that happens, it becomes almost impossible to reverse the event, since classical information can be replicated indefinitely and so becomes very difficult to "unwind." That near-impossibility of reversal is what we call causality, and on the scale we live, it really is a one-way street.
In the case of your problem, the envelope of uncertainty is the orientation of the Bob electron. It must remain unknown to remain quantum, so the problem must be such that the high magnetic field gradient (you are really talking about a Stern-Gerlach I think) cannot already know the orientation of the electron. Without already knowing that orientation, it also cannot "see" a change in that orientation.
Feynman has a great discussion on trying to "trick" QM into violating this historical/quantum boundary, one that tries to "see" which slit an electron goes through in a self-interference experiment. I think that was in QED, but it may have been in his Lectures; I'll look up the reference an add it here shortly.