The equation describing a capacitor is I=C*dV/dt, or in non-geek-speak: "The instantaneous current through the capacitor equals the capacitance, times the rate of change of voltage."
So, if a capacitor datasheet gives a maximum dv/dt rating, it is usually a peak current rating in disguise. In your case, say your capacitor was 100uF:
I=100e-6 * 14/1e-6 = 1400A which is far more than any tube amp PT I've ever seen is capable of providing under any circumstances, except maybe a direct lightning strike
You may want to redo this calculation with the actual capacitance, but the conclusion shouldn't change: these capacitors are designed for heavy-duty use in switchmode power supplies that subject them to far more abuse than a tube amplifier could.