Do MRI magnets oscillate due to parasitic capacitance?
The only problem that an LC resonance would introduce is some ringing at discontinuities.

You may rest assured that we treat changing the field of a superconducting magnet in much the same way that you would do dental work on a nuclear polecat; very, very carefully and slowly. The economic cost, and physical danger, of a quench that could result from messing the process up is too high.

The process is (a) ramp up the current into the superconducting switch, until the external driven current matches the magnet current (b) open the switch (c) ramp the current to the new value (d) close the switch.

We take much precaution before step (b), as the voltage generated by the residual delta current could exceed the insulation rating of the magnet. Any ringing due to self capacitance is completely irrelevant, the damage will have been done in that first excursion. In fact, the self capacitance is a mitigating feature, that voltage spike has to charge the self capacitance, and so it limits the voltage.