No, that's not what happens. It is without doubt the magnetic field that rearranges its topology
before the change in currents. The energy lost to the field is transferred to kinetic energy of the plasma. Electric currents
by themselves cannot all gain energy, that clearly violates the fundamental conservation of energy principle. Rather, there has to be a mix of currents & magnetic fields, and there has to be a transfer of energy from the field to the current. That transfer of energy cannot come from common induction because the time scale for that is too long (see, e.g.,
Magnetic Reconnection Redux V). A rearrangement in the topology of the magnetic field, which can release energy on a much shorter time scale consistent with observation, is the only alternative physical process available. And since we can observe it to happen
in situ in laboratory plasma experiments, despite Mozina's erroneous claims to the contrary, and since there is copious evidence for magnetic reconnection in observed astrophysical plasma (see, e.g.,
Magnetic Reconnection Redux XI), it's the obvious way to go.
No, this is exactly the opposite of what really happens. The magnetic field drives the process and the current goes along for the ride. The field changes
first and the currents gain energy
second, in that specific order. If the currents were actually driving the process, it would work the other way around.