Do magnetic fields generated from ion flow through a membrane channel have any physiological relevance?
For currents in biological systems the magnetic field is minuscule, and likely has no physiological effect.

That said, magnetoencephalography is based on measuring the tiny magnetic fields created when nerves fire. Detection requires an incredibly sensitive detector, a superconducting quantum interference device (SQUID), to detect the location of the currents. A SQUID can detect fields of just a few atoteslas (aT)!

Perhaps one could investigate how much ion flow in electric eel muscle is constrained by the induced magnetic field... It could lead to shocking revelations.