Question on capacitive circuit in practice

If we were to build a circuit, let's say with a power source of 120V AC going into a transformer which steps that up to 10kV @ 30mA, the output of which would be connected to a capacitor with a capacitance of about 3060pF, what would be happening in that circuit, especially on the right side, where the capacitor is, if 60 Hz were pumped in there through the AC source, taking into account where the circuit is grounded?

Now, theoretically from what I understand, due to the fact that the right side would act as a purely capacitive circuit, there would be "no power" because the current and voltage are 90 degrees out of phase. However, if I were to build this, would something blow or burn up or quit working, like the transformer or the capacitor or the wire? Would AC flowing through a capacitor count as a no-load situation and mess up the transformer? Also, would it be necessary to ground it twice? I'm just wondering how this would function were I to build this circuit, and what I technically should/could design better.